**Simulation of 3-D Coastal Spit Geomorphology Using Differential Synthetic Aperture Interferometry (DInSAR)**

Maged Marghany

*Institute for Science and Technology Geospatial (INSTEG) Universiti Teknologi Malaysia, Skudai, Johor Bahru, Malaysia* 

### **1. Introduction**

82 Recent Interferometry Applications in Topography and Astronomy

F. Casu, M. Manzo, A. Pepe, and R. Lanari, "SBAS-DInSAR Analysis of Very Extended

L. P. Chew, "Constrained Delaunay triangulations," in Algorithmica, vol. 4, Springer.

Lett., vol. 5, no. 3, pp. 438-442, Jul. 2008.

Verlag. New York 1989, pp. 97–108.

Areas: First Results on a 60000-km2 Test Site," IEEE Geosci. and Remote Sensing

Interferometric synthetic aperture radar (InSAR or IfSAR), is a geodetic technique uses two or more single look complex synthetic aperture radar (SAR) images to produce maps of surface deformation or digital elevation (Massonnet, and Feigl 1998; Burgmann et al., 2000; Hanssen 2001). It has applications as well, for monitoring of geophysical natural hazards, for instance earthquakes, volcanoes and landslides, also in engineering, in particular recording of subsidence and structural stability. Over time-spans of days to years, InSAR can detect the centimetre-scale of deformation changes (Zebker et al.,1997). Further, the precision DEMs with of a couple of ten meters can produce from InSAR technique compared to conventional remote sensing methods. Nevertheless, the availability of the precision DEMs may a cause of two-pass InSAR; regularly 90 m SRTM data may be accessible for numerous territories (Askne et al.,2003). InSAR, consequently, provides DEMs with 1-10 cm accuracy, which can be improved to millimetre level by DInSAR. Even so, alternative datasets must acquire at high latitudes or in areas of rundown coverage (Nizalapur et al., 2011). However, the baseline decorrelation and temporal decorrelation make InSAR measurements unfeasible (Lee 2001; Luo et al., 2006; Yang et al., 2007; Rao and Jassar 2010). In this regard, Gens (2000) reported the length of the baseline designates the sensitivity to height changes and sum of baseline decorrelation. Further, Gens (2000) stated the time difference for two data acquisitions is a second source of decorrelation. Indeed, the time differences while comparing data sets with a similar baseline length acquired one and 35 days a part suggests only the temporal component of the decorrelation. Therefore, the loss of coherence in the same repeat cycle in data acquisition are most likely because of baseline decorrelation. According to Roa et al. (2006), uncertainties could arise in DEM because of limitation InSAR repeat passes. In addition, the interaction of the radar signal with troposphere can also induce decorrelation. This is explained in several studies of Hanssen (2001); Marghany and Hashim (2009); and Rao and Jassar (2010).

Generally, the propagation of the waves through the atmosphere can be a source of error exist in most interferogram productions. When the SAR signal propagated through a

Simulation of 3-D Coastal Spit Geomorphology

Fig. 1. Location of spit along Kuala Terengganu river mouth.

more frequent basis (RADARSAT 2011).

**3.2 Ground data** 

**3. Data sets 3.1 Satellite data** 

Using Differential Synthetic Aperture Interferometry (DInSAR) 85

In the present study, RADARSAT-1 SAR data sets of 23 November 1999 (SLC-1), 23 December 2003 (SLC-2) and March 26, 2005, (SLC-3) of Fine mode data (F1) are implemented. These data are C-band and had the lower signal-to-noise ratio owing to their HH polarization with wavelength of 5.6 cm and frequency of 5.3 GHz. The Fine beam mode is intended for applications which require the best spatial resolution available from the RADARSAT-1 SAR system. The azimuth resolution is 8.4 m, and range resolution ranges between 9.1 m to 7.8 m. Originally, five Fine beam positions, F1 to F5, are available to cover the far range of the swath with incidence angle ranges from 37° to 47°. By modifying timing parameters, 10 new positions have been added with offset ground coverage. Each original Fine beam position can either be shifted closer to or farther away from Nadir. The resulting positions are denoted by either an N (Near) or F (Far). For example, F1 is now complemented by F1N and F1F (RADARSAT 2011). Finally, RADARSAT-1 requires 24 days to return to its original orbit path. This means that for most geographic regions, it will take 24 days to acquire exactly the same image (the same beam mode, position, and geographic coverage). However, RADARSAT's imaging flexibility allows images to be acquired on a

Following Marghany et al., (2010b), the GPS survey used to: (i) to record exact geographical position of shoreline; (ii) to determine the cross-sections of shore slopes; (iii) to corroborate the reliability of DInSAR data co-registered; and finally, (iv) to create a reference network for future surveys. The geometric location of the GPS survey was obtained by using the new

vacuum it should theoretically be subjected to some decent accuracy of timing and cause phase delay (Hanssen 2001). A constant phase difference between the two images caused by the horizontally homogeneous atmosphere was over the length scale of an interferogram and vertically over that of the topography. The atmosphere, however, is laterally heterogeneous on length scales both larger and smaller than typical deformation signals (Lee 2001). In other cases the atmospheric phase delay, however, is caused by vertical inhomogeneity at low altitudes and this may result in fringes appearing to correspond with the topography. Under this circumstance, this spurious signal can appear entirely isolated from the surface features of the image, since the phase difference is measured other points in the interferogram, would not contribute to the signal (Hanssen 2001). This can reduce seriously the low signal-to-noise ratio (SNR) which restricted to perform phase unwrapping. Accordingly, the phases of weak signals are not reliable. According to Yang et al., (2007), the correlation map can be used to measure the intensity of the noise in some sense. It may be overrated because of an inadequate number of samples allied with a small window (Lee 2001). Weights are initiated to the correlation coefficients according to the amplitudes of the complex signals to estimate accurate reliability (Yang et al., 2007).

### **1.1 Hypothesis and objective of study**

Concerning with above prospective, we address the question of decorrelation uncertainties impact on modelling Digital Elevation Model (DEM) for 3-D coastal spit visualization from DInSAR technique. This is demonstrated with RADARSAT-1 fine mode data (F1) using fuzzy B-spline algorithm. Taking advantage of the fact that fuzzy B-spline can use for solving uncertainty problem because of decorrelation and the low signal-to-noise ratio (SNR) in data sets. This work hypothesises that integration of fuzzy B-spline algorithm with phase unwrapping can produce accurately digital elevation of object deformation (Marghany et al., 2010a and Marghany 2012). The aim of this paper is to explore the precision of the digital elevation models (DEM) derived from RADARSAT-1 fine mode data (F1) and, thus, the potential of the sensor for mapping coastal geomorphologic feature changes. Depending on the results, a wider application of F1 mode data for the study of Kuala Terengganu mouth river landscapes is envisaged.

### **2. Study area**

The study area is selected along the mouth river of Kuala Terengganu, Malaysia. According to Marghany et al., (2010a) the coastline appears to be linear and oriented at about 45° along the east coast of Malaysia (Marghany et al. 2010b). In addition, spit was located across the largest hydrological communications between the estuary and the South China Sea the i.e. mouth river of Kuala Terengganu (Fig. 1) which lies on the equatorial region, and is affected by monsoon winds (Marghany and Mazlan 2010a,b). Indeed, during the northeast monsoon period, the strong storm and wave height of 4 m can cause erosion (Marghany et al. 2010b). The 20 km stretches of coastal along the Kuala Terengganu shoreline composed of sandy beach, the somewhat most frequently eroded region. The significant source of sediment is from the Terengganu River which loses to the continental shelf due to the complex movements of waves approached from the north direction (Marghany et al. 2010b).

Fig. 1. Location of spit along Kuala Terengganu river mouth.

### **3. Data sets**

84 Recent Interferometry Applications in Topography and Astronomy

vacuum it should theoretically be subjected to some decent accuracy of timing and cause phase delay (Hanssen 2001). A constant phase difference between the two images caused by the horizontally homogeneous atmosphere was over the length scale of an interferogram and vertically over that of the topography. The atmosphere, however, is laterally heterogeneous on length scales both larger and smaller than typical deformation signals (Lee 2001). In other cases the atmospheric phase delay, however, is caused by vertical inhomogeneity at low altitudes and this may result in fringes appearing to correspond with the topography. Under this circumstance, this spurious signal can appear entirely isolated from the surface features of the image, since the phase difference is measured other points in the interferogram, would not contribute to the signal (Hanssen 2001). This can reduce seriously the low signal-to-noise ratio (SNR) which restricted to perform phase unwrapping. Accordingly, the phases of weak signals are not reliable. According to Yang et al., (2007), the correlation map can be used to measure the intensity of the noise in some sense. It may be overrated because of an inadequate number of samples allied with a small window (Lee 2001). Weights are initiated to the correlation coefficients according to the

amplitudes of the complex signals to estimate accurate reliability (Yang et al., 2007).

Concerning with above prospective, we address the question of decorrelation uncertainties impact on modelling Digital Elevation Model (DEM) for 3-D coastal spit visualization from DInSAR technique. This is demonstrated with RADARSAT-1 fine mode data (F1) using fuzzy B-spline algorithm. Taking advantage of the fact that fuzzy B-spline can use for solving uncertainty problem because of decorrelation and the low signal-to-noise ratio (SNR) in data sets. This work hypothesises that integration of fuzzy B-spline algorithm with phase unwrapping can produce accurately digital elevation of object deformation (Marghany et al., 2010a and Marghany 2012). The aim of this paper is to explore the precision of the digital elevation models (DEM) derived from RADARSAT-1 fine mode data (F1) and, thus, the potential of the sensor for mapping coastal geomorphologic feature changes. Depending on the results, a wider application of F1 mode data for the study of

The study area is selected along the mouth river of Kuala Terengganu, Malaysia. According to Marghany et al., (2010a) the coastline appears to be linear and oriented at about 45° along the east coast of Malaysia (Marghany et al. 2010b). In addition, spit was located across the largest hydrological communications between the estuary and the South China Sea the i.e. mouth river of Kuala Terengganu (Fig. 1) which lies on the equatorial region, and is affected by monsoon winds (Marghany and Mazlan 2010a,b). Indeed, during the northeast monsoon period, the strong storm and wave height of 4 m can cause erosion (Marghany et al. 2010b). The 20 km stretches of coastal along the Kuala Terengganu shoreline composed of sandy beach, the somewhat most frequently eroded region. The significant source of sediment is from the Terengganu River which loses to the continental shelf due to the complex movements of waves approached from the north direction (Marghany et al. 2010b).

**1.1 Hypothesis and objective of study** 

Kuala Terengganu mouth river landscapes is envisaged.

**2. Study area** 

### **3.1 Satellite data**

In the present study, RADARSAT-1 SAR data sets of 23 November 1999 (SLC-1), 23 December 2003 (SLC-2) and March 26, 2005, (SLC-3) of Fine mode data (F1) are implemented. These data are C-band and had the lower signal-to-noise ratio owing to their HH polarization with wavelength of 5.6 cm and frequency of 5.3 GHz. The Fine beam mode is intended for applications which require the best spatial resolution available from the RADARSAT-1 SAR system. The azimuth resolution is 8.4 m, and range resolution ranges between 9.1 m to 7.8 m. Originally, five Fine beam positions, F1 to F5, are available to cover the far range of the swath with incidence angle ranges from 37° to 47°. By modifying timing parameters, 10 new positions have been added with offset ground coverage. Each original Fine beam position can either be shifted closer to or farther away from Nadir. The resulting positions are denoted by either an N (Near) or F (Far). For example, F1 is now complemented by F1N and F1F (RADARSAT 2011). Finally, RADARSAT-1 requires 24 days to return to its original orbit path. This means that for most geographic regions, it will take 24 days to acquire exactly the same image (the same beam mode, position, and geographic coverage). However, RADARSAT's imaging flexibility allows images to be acquired on a more frequent basis (RADARSAT 2011).

### **3.2 Ground data**

Following Marghany et al., (2010b), the GPS survey used to: (i) to record exact geographical position of shoreline; (ii) to determine the cross-sections of shore slopes; (iii) to corroborate the reliability of DInSAR data co-registered; and finally, (iv) to create a reference network for future surveys. The geometric location of the GPS survey was obtained by using the new

Simulation of 3-D Coastal Spit Geomorphology

For an exceptional case where *<sup>R</sup>*

unwrapping phase as follow,

where ( ) ,4 *p* 

Marghany (2011) as

[ , ]

displacement as

Using Differential Synthetic Aperture Interferometry (DInSAR) 87

Incorporating equations 2 and 3 gives the phase difference, only from the surface

<sup>4</sup>

unwrapping may not be necessary (Massonnet et al., 1998). However, this is not practical and it is difficult to achieve from the system design for a repeat-pass interferometer. From

*M d ij ij*

( , ) ( , ) ( , ) ( , )

where *S* (*i*, *j*) *<sup>M</sup>* and *S* (*i*, *j*) *<sup>s</sup>* are master and slave complex data while <sup>1</sup>

*knot q*=[0,0,0,0,1,2,3,….,*M,M,M,M*]. Fourth the order B-spline basis are used (.)

**5. Three-dimensional SPIT visualization using DInSAR technique** 

*S i j S i j S i j S i j*

*M s M s*

*ij*

thresholds. The curve points *S(p,q)* are affected by { } *wij*

,4 ,4

*m l ml*

( ) ( )

*p q w*

control net and { } *wij* is the weighted correlation coefficient which was estimated based on

2 1

*t t*

<sup>1</sup> ' *<sup>j</sup> <sup>j</sup> <sup>P</sup> q r r* , where *P* and *P'* are the degree of the two B-spline basis functions constituted the B-spline surface. Two sets of knot vectors are knot *p*=[0,0,0,0,1,2,3,……,*O,O,O,O*], and

the continuity of the tangents and curvatures on the whole surface topology including at the

The new fuzzy B-spline formula for 3D coastal features' reconstruction from DInSAR retrieved unwrapping phase was trained on three RADARSAT-1 SAR fine mode data (Fig.2). The master data was acquired on 23 November 1999, the slave 1 data was acquired on 23 December 2003, while slave 2 data acquisition was on 26 March 2005, respectively. The

,4 ,4 ,

( ) ( )

*d ij i j i j*

*C p q w*

Marghany and Mazlan (2009) introduces a method to construct 3-D object visualisation from

<sup>4</sup>

*R* 

equation 4 the displacement sensitivity of DInSAR is given as

*O*

*l*

0 0

*m*

*j*

0 0

*O*

*M*

*i*

*S p q*

*<sup>i</sup>* and ( ) ,4 *q* 

*w*

patches' boundaries (Marghany 2011).

( , )

*d*

 *<sup>R</sup> R*

in equation 4 there is a positive integer number, phase

*O*

*M*

*i*

*<sup>j</sup>* are two bases of B-spline functions, { } *Cij* is the bidirectionally

<sup>1</sup> <sup>2</sup> <sup>2</sup> min( ( , ), ( , ))

*x S i j S i j t*

*M s*

*j*

0 0

*<sup>d</sup>* . (5)

*C S p q*

( , )

in case of [ , ] *<sup>i</sup> <sup>i</sup> <sup>P</sup>*<sup>1</sup> *p r r* and

(6)

(7)

*t* and 2*t* are

*<sup>j</sup>*,4 to ensure

. (4)

satellite geodetic network, IGM95. After a careful analysis of the places and to identify the reference vertexes, we thickened the network around such vertexes to perform the measurements for the cross sections (transact perpendicular to the coastline). The GPS data collected within 20 sample points scattered along 400 m coastline. The interval distance of 20 m between sample location is considered. In every sample location, Rec-Alta (Recording Electronic Tacheometer) was used to acquire the spit elevation profile. The ground truth data were acquired on 23 December 2003 March 26, 2005, during satellite passes. Then ground data used to validate and find out the level of accuracy for DInSAR and fuzzy Bspline algorithm.

### **4. DInSAR data processing**

The DInSAR technique measures the block displacement of land surface caused by subsidence, earthquake, glacier movement, and volcano inflation to cm or even mm accuracy (Luo et al., 2006). According to Lee (2001), the surface displacement can estimate using the acquisition times of two SAR images *S*1 and *S*<sup>2</sup> . The component of surface displacement thus, in the radar-look direction, contributes to further interferometric phase (φ ) as

$$
\phi\_{\parallel} = \frac{4\,\pi}{\lambda} (\Delta R\_{\parallel} + \zeta\_{\parallel}) \tag{1}
$$

where *R* is the slant range difference from satellite to target respectively at different time, is the RADARSAT-1 SAR fine mode wavelength which is about 5.6 cm for CHH- band. According to Lee (2001), for the surface displacement measurement, the zero-baseline InSAR configuration is the ideal as *R* 0 , so that

$$
\phi = \phi\_d = \frac{4\pi}{\lambda} \mathcal{L} \tag{2}
$$

In practice, zero-baseline, repeat-pass InSAR configuration is hardly achievable for either spaceborne or airborne SAR. Therefore, a method to remove the topographic phase as well as the system geometric phase in a non-zero baseline interferogram is needed. If the interferometric phase from the InSAR geometry and topography can strip of from the interferogram, the remnant phase would be the phase from block surface movement, providing the surface maintains high coherence (Luo et al., 2006).

Zebker et al. (1994) and Luo et al., (2006) used the three-pass method to remove topographic phase from the interferogram. This method requires a reference interferogram, which is promised to contain the topographic phase only. The three-pass approach has the advantage in that all data is kept within the SAR data geometry while DEM method can produce errors by misregistration between SAR data and cartographic DEM. The three-pass approach is restricted by the data availability. The three-passes DInSAR technique uses another InSAR pair as a reference interferogram that does not contain any surface movement event as

$$
\phi' = \frac{4\pi}{\lambda} \Delta R' \cdot \tag{3}
$$

satellite geodetic network, IGM95. After a careful analysis of the places and to identify the reference vertexes, we thickened the network around such vertexes to perform the measurements for the cross sections (transact perpendicular to the coastline). The GPS data collected within 20 sample points scattered along 400 m coastline. The interval distance of 20 m between sample location is considered. In every sample location, Rec-Alta (Recording Electronic Tacheometer) was used to acquire the spit elevation profile. The ground truth data were acquired on 23 December 2003 March 26, 2005, during satellite passes. Then ground data used to validate and find out the level of accuracy for DInSAR and fuzzy B-

The DInSAR technique measures the block displacement of land surface caused by subsidence, earthquake, glacier movement, and volcano inflation to cm or even mm accuracy (Luo et al., 2006). According to Lee (2001), the surface displacement can estimate using the acquisition times of two SAR images *S*1 and *S*<sup>2</sup> . The component of surface displacement thus, in the radar-look direction, contributes to further interferometric phase

( ) <sup>4</sup>

*<sup>R</sup>*

where *R* is the slant range difference from satellite to target respectively at different time,

 is the RADARSAT-1 SAR fine mode wavelength which is about 5.6 cm for CHH- band. According to Lee (2001), for the surface displacement measurement, the zero-baseline InSAR

In practice, zero-baseline, repeat-pass InSAR configuration is hardly achievable for either spaceborne or airborne SAR. Therefore, a method to remove the topographic phase as well as the system geometric phase in a non-zero baseline interferogram is needed. If the interferometric phase from the InSAR geometry and topography can strip of from the interferogram, the remnant phase would be the phase from block surface movement,

Zebker et al. (1994) and Luo et al., (2006) used the three-pass method to remove topographic phase from the interferogram. This method requires a reference interferogram, which is promised to contain the topographic phase only. The three-pass approach has the advantage in that all data is kept within the SAR data geometry while DEM method can produce errors by misregistration between SAR data and cartographic DEM. The three-pass approach is restricted by the data availability. The three-passes DInSAR technique uses another InSAR pair as a reference interferogram that does not contain any surface

> *R*

4 . (3)

 <sup>4</sup> *<sup>d</sup>*

providing the surface maintains high coherence (Luo et al., 2006).

 (1)

(2)

spline algorithm.

(φ ) as

movement event as

**4. DInSAR data processing** 

configuration is the ideal as *R* 0 , so that

Incorporating equations 2 and 3 gives the phase difference, only from the surface displacement as

$$
\phi\_d = \phi - \frac{\Delta R}{\Delta R'} \phi' = \frac{4\pi}{\lambda} \zeta'. \tag{4}
$$

For an exceptional case where *<sup>R</sup> R* in equation 4 there is a positive integer number, phase unwrapping may not be necessary (Massonnet et al., 1998). However, this is not practical and it is difficult to achieve from the system design for a repeat-pass interferometer. From equation 4 the displacement sensitivity of DInSAR is given as

$$\frac{\partial \phi\_d}{\partial \zeta} = \frac{4\pi}{\lambda} \cdot \tag{5}$$

Marghany and Mazlan (2009) introduces a method to construct 3-D object visualisation from unwrapping phase as follow,

$$S(p,q) = \frac{\sum\_{l=0}^{M} \sum\_{j=0}^{O} \phi\_d C\_{y,l} \beta\_{l,4}(p) \beta\_{j,4}(q) w\_{l,j}}{\sum\_{m=0}^{M} \sum\_{l=0}^{O} \beta\_{m,4}(p) \beta\_{l,4}(q) w\_{ml}} = \sum\_{l=0}^{M} \sum\_{j=0}^{O} \phi\_d C\_{y} S\_{y}(p,q) \tag{6}$$

where ( ) ,4 *p <sup>i</sup>* and ( ) ,4 *q <sup>j</sup>* are two bases of B-spline functions, { } *Cij* is the bidirectionally control net and { } *wij* is the weighted correlation coefficient which was estimated based on Marghany (2011) as

$$\mathbf{w}\_{\boldsymbol{y}} = \frac{\left| \frac{\sum S\_M(i, j) S\_s(i, j)}{\sqrt{\sum \left| S\_M(i, j) \right|^2 \sum \left| S\_s(i, j) \right|^2}} \right| \text{x} \min(\left| S\_M(i, j) \right| \left| S\_s(i, j) \right|) - t\_1}{t\_2 - t\_1} \tag{7}$$

where *S* (*i*, *j*) *<sup>M</sup>* and *S* (*i*, *j*) *<sup>s</sup>* are master and slave complex data while <sup>1</sup> *t* and 2*t* are thresholds. The curve points *S(p,q)* are affected by { } *wij* in case of [ , ] *<sup>i</sup> <sup>i</sup> <sup>P</sup>*<sup>1</sup> *p r r* and [ , ] <sup>1</sup> ' *<sup>j</sup> <sup>j</sup> <sup>P</sup> q r r* , where *P* and *P'* are the degree of the two B-spline basis functions constituted the B-spline surface. Two sets of knot vectors are knot *p*=[0,0,0,0,1,2,3,……,*O,O,O,O*], and *knot q*=[0,0,0,0,1,2,3,….,*M,M,M,M*]. Fourth the order B-spline basis are used (.) *<sup>j</sup>*,4 to ensure the continuity of the tangents and curvatures on the whole surface topology including at the patches' boundaries (Marghany 2011).

### **5. Three-dimensional SPIT visualization using DInSAR technique**

The new fuzzy B-spline formula for 3D coastal features' reconstruction from DInSAR retrieved unwrapping phase was trained on three RADARSAT-1 SAR fine mode data (Fig.2). The master data was acquired on 23 November 1999, the slave 1 data was acquired on 23 December 2003, while slave 2 data acquisition was on 26 March 2005, respectively. The

Simulation of 3-D Coastal Spit Geomorphology

Using Differential Synthetic Aperture Interferometry (DInSAR) 89

Fig. 3. Variation of (a) coherence and (b) ratio coherence in F1 mode data.

**Acquisition Data Baseline Wind Speed** 

345

266

400

Table 1. Baseline estimations with wind and tidal conditions during acquisition time.

Evidently, wind speed of 11 m/s affects the scattering from certain vegetation classes and sandy regions and consequently produce poor coherence (Table 1). The overall scene is highly incoherent, not only because of the meteorological conditions and the vegetation cover at the time but also because of ocean surface turbulent changes. This decorelation caused poor detection of spit which induce large ambiguities because of poor coherence and scattering phenomenology. The ground ambiguity and ideal assumption that volume-only coherence can be acquired in at least one polarization. This assumption may fail when vegetation is thick, dense, or the penetration of electromagnetic wave is weak. This is agreed

Fig. 4 shows the interferogram created from F1 data. For three data sets, only small portion of the scene processed because of temporal decorrelation. According to Luo et al.,(2007), the SAR interferogram is considered to be difficult to unwrap because of its large areas of low

acquisition are most likely because of baseline decorrelation.

23 November 1999

23 December 2003

26 March 2005

with study of Lee (2001).

the decorrelation. Therefore, the loss of coherence in the same repeat cycle in data

**(m/s) Tidal (m)** 

1.2

1.5

1.8

7.3

9

11

master data was ascending while both slave data were descending. Figure 2 shows the variation of the backscatter intensity for the F1 mode data along Terengganu's estuary. The urban areas have the highest backscatter of-10 dB as compared to water body and the vegetation area (Fig. 2).

Fig. 2. RADARSAT-1 SAR fine mode data acquisition (a) master data, (b) data slave 1 data and (c ) slave 2 data.

It is interesting to find the coherence image coincided with backscatter variation along the coastal zone. Fig. 3(a) shows that urban zone dominated with higher coherence of 0.8 than vegetation and sand areas. The coastal spit has lower backscatter and coherence of 0.3 dB and 0.25, respectively. Since three F1 mode data acquired in wet north-east monsoon period, there is an impact of wet sand on radar signal penetration which causing weak penetration of radar signal because of dielectric. Figure 3b shows the ratio coherence image, clearly the total topographic decorrelation effects along the radar-facing slopes are dominant and highlighted as bright features of 3 over a grey background. This is caused by the microscale movement of the sand particles driven by the coastal hydrodynamic, and wind continuously changes the distribution of scatterers resulting in rapid temporal decorrelation which has contributed to decorrelation in the spit zone.

Clearly, the random changes in the surface scatterer locations among data acquisitions with a wavelength of 5.6 cm for C-band are sufficient to decorrelate the interferometric signal. Under this circumstance, it will be visible in the coherence data (Fig.3). Since vegetation and wet sand changes may also reduce the coherence because the estuary area has tides and water lines that are so highly variable, this can be defined in fuzzy or probabilistic terms. The geomorphology feature of spit is rendered meaningless or unreliable in the long term because of their high variability. This confirms the studies of of Hanssen (2001); Marghany and Hashim (2009); and Rao and Jassar (2010); Marghany (2011).

Further, the estimated baseline is varied between master data and both slave data. The estimated baseline between master data and second slave data is 400 m which is larger than slave 1 data (Table 1). In this context, Gens (2000) reported the length of the baseline designates the sensitivity to height changes and sum of baseline decorrelation. Further, Nizalapur et al., (2011) stated the time difference for two data acquisitions is a second source of decorrelation. Indeed, the time difference while comparing data sets with a similar baseline length acquired one and 35 days a part suggest only the temporal component of

master data was ascending while both slave data were descending. Figure 2 shows the variation of the backscatter intensity for the F1 mode data along Terengganu's estuary. The urban areas have the highest backscatter of-10 dB as compared to water body and the

Fig. 2. RADARSAT-1 SAR fine mode data acquisition (a) master data, (b) data slave 1 data

It is interesting to find the coherence image coincided with backscatter variation along the coastal zone. Fig. 3(a) shows that urban zone dominated with higher coherence of 0.8 than vegetation and sand areas. The coastal spit has lower backscatter and coherence of 0.3 dB and 0.25, respectively. Since three F1 mode data acquired in wet north-east monsoon period, there is an impact of wet sand on radar signal penetration which causing weak penetration of radar signal because of dielectric. Figure 3b shows the ratio coherence image, clearly the total topographic decorrelation effects along the radar-facing slopes are dominant and highlighted as bright features of 3 over a grey background. This is caused by the microscale movement of the sand particles driven by the coastal hydrodynamic, and wind continuously changes the distribution of scatterers resulting in rapid temporal decorrelation

Clearly, the random changes in the surface scatterer locations among data acquisitions with a wavelength of 5.6 cm for C-band are sufficient to decorrelate the interferometric signal. Under this circumstance, it will be visible in the coherence data (Fig.3). Since vegetation and wet sand changes may also reduce the coherence because the estuary area has tides and water lines that are so highly variable, this can be defined in fuzzy or probabilistic terms. The geomorphology feature of spit is rendered meaningless or unreliable in the long term because of their high variability. This confirms the studies of of Hanssen (2001); Marghany

Further, the estimated baseline is varied between master data and both slave data. The estimated baseline between master data and second slave data is 400 m which is larger than slave 1 data (Table 1). In this context, Gens (2000) reported the length of the baseline designates the sensitivity to height changes and sum of baseline decorrelation. Further, Nizalapur et al., (2011) stated the time difference for two data acquisitions is a second source of decorrelation. Indeed, the time difference while comparing data sets with a similar baseline length acquired one and 35 days a part suggest only the temporal component of

which has contributed to decorrelation in the spit zone.

and Hashim (2009); and Rao and Jassar (2010); Marghany (2011).

vegetation area (Fig. 2).

and (c ) slave 2 data.

Fig. 3. Variation of (a) coherence and (b) ratio coherence in F1 mode data.

the decorrelation. Therefore, the loss of coherence in the same repeat cycle in data acquisition are most likely because of baseline decorrelation.


Table 1. Baseline estimations with wind and tidal conditions during acquisition time.

Evidently, wind speed of 11 m/s affects the scattering from certain vegetation classes and sandy regions and consequently produce poor coherence (Table 1). The overall scene is highly incoherent, not only because of the meteorological conditions and the vegetation cover at the time but also because of ocean surface turbulent changes. This decorelation caused poor detection of spit which induce large ambiguities because of poor coherence and scattering phenomenology. The ground ambiguity and ideal assumption that volume-only coherence can be acquired in at least one polarization. This assumption may fail when vegetation is thick, dense, or the penetration of electromagnetic wave is weak. This is agreed with study of Lee (2001).

Fig. 4 shows the interferogram created from F1 data. For three data sets, only small portion of the scene processed because of temporal decorrelation. According to Luo et al.,(2007), the SAR interferogram is considered to be difficult to unwrap because of its large areas of low

Simulation of 3-D Coastal Spit Geomorphology

Fig. 6. DEM of coastal spit.

Using Differential Synthetic Aperture Interferometry (DInSAR) 91

Fig. 6 represents 3-D spit reconstruction using fuzzy B-spline with the maximum spit 's elevation is 3 m with gentle slope of 0.86 m. The rate change of spit is 3 m/year with maximum elevation height of 2.4 m (Figs 5 and 6). Clearly, Terengganu 's spit was generated due to the deposition of sediment due to hydrodynamic changes between estuary and ocean. According to Marghany (2012) Terengganu 's mouth river is the largest hydrologic communication between an estuary and the South China Sea. This spit occurred when longshore drift reaches a section of Terengganu's River where the turn is greater than 30 degrees. It continued out therefore, into the sea until water pressure from a Terengganu 's River becomes too much to allow the sand to deposit. The spit be then grown upon and become stable and often fertile. As spit grows, the water behind them is sheltered from wind and waves. This could be due the high sediment transport through the water outflow from the river mouth, or northerly net sediment transport due to northeast monsoon wave effects (Marghany et al., 2010b). Longshore drift (also called littoral drift) occurs due to waves meeting the beach at an oblique angle, and back washing perpendicular to the shore, moving sediment down the beach in a zigzag pattern. Longshore drifting is complemented by longshore currents, which transport sediment through the water alongside the beach. These currents are set in motion by the same oblique angle of entering waves that cause littoral drift and transport sediment in a similar process. The hydrodynamic interaction between the longshore current and water inflow from the Terengganu Mouth River is causing the changes in spit's geomorphology characteristics. This finding confirms the study of Marghany et al., (2010a) ; Marghany et al., (2010b) and Marghany (2011). The increasing growth of spit across the estuary is due to impact of sedimentation due to littoral drift. According to Marghany and Mazlan (2010a) net littoral drift along Kuala Terengganu coastal water is towards the southward which could induce the growth of spit length.

Finally, a difference statistical comparison confirms the results of Figs 4,5 and 6. Table 2 shows the statistical comparison between the simulated DEM from the DInSAR, real ground measurements and with using fuzzy B-spline. This table represents the bias (averages mean the standard error, 90 and 95% confidence intervals, respectively. Evidently, the DInSAR

coherence, which caused by temporal decorrelation. These areas of low coherence segment the interferogram into many pieces, which creates difficulties for the unwrapping algorithms (Fig.4). In this context, Lee (2001) reported that when creating an interferogram of surface deformation by using InSAR, it is not always true that an interference pattern (fringes) of an initial interferogram directly shows surface deformation. Indeed, the difference in phase between two observations is influenced by things outside surface deformation.

Fig. 4. Interfeorgram generated from F1 mode data.

Figure 5 shows the interferogram created using fuzzy B-spline algorithm. The full color cycle represents a phase cycle, covering range between –π to π. In this context, the phase difference given module 2 π; is color encoded in the fringes. Seemingly, the color bands change in the reverse order, indicating that the center has a great deformation along the spit. This shift corresponds to 0.4 centimetres (cm) of coastal deformation over the distance of 500 m. The urban area dominated by deformation of 2.8 cm.

Fig. 5. Fringe Interferometry generated by fuzzy B-spline.

coherence, which caused by temporal decorrelation. These areas of low coherence segment the interferogram into many pieces, which creates difficulties for the unwrapping algorithms (Fig.4). In this context, Lee (2001) reported that when creating an interferogram of surface deformation by using InSAR, it is not always true that an interference pattern (fringes) of an initial interferogram directly shows surface deformation. Indeed, the difference in phase between two observations is influenced by things outside surface

Figure 5 shows the interferogram created using fuzzy B-spline algorithm. The full color cycle represents a phase cycle, covering range between –π to π. In this context, the phase difference given module 2 π; is color encoded in the fringes. Seemingly, the color bands change in the reverse order, indicating that the center has a great deformation along the spit. This shift corresponds to 0.4 centimetres (cm) of coastal deformation over the distance

deformation.

Fig. 4. Interfeorgram generated from F1 mode data.

of 500 m. The urban area dominated by deformation of 2.8 cm.

Fig. 5. Fringe Interferometry generated by fuzzy B-spline.

Fig. 6 represents 3-D spit reconstruction using fuzzy B-spline with the maximum spit 's elevation is 3 m with gentle slope of 0.86 m. The rate change of spit is 3 m/year with maximum elevation height of 2.4 m (Figs 5 and 6). Clearly, Terengganu 's spit was generated due to the deposition of sediment due to hydrodynamic changes between estuary and ocean. According to Marghany (2012) Terengganu 's mouth river is the largest hydrologic communication between an estuary and the South China Sea. This spit occurred when longshore drift reaches a section of Terengganu's River where the turn is greater than 30 degrees. It continued out therefore, into the sea until water pressure from a Terengganu 's River becomes too much to allow the sand to deposit. The spit be then grown upon and become stable and often fertile. As spit grows, the water behind them is sheltered from wind and waves. This could be due the high sediment transport through the water outflow from the river mouth, or northerly net sediment transport due to northeast monsoon wave effects (Marghany et al., 2010b). Longshore drift (also called littoral drift) occurs due to waves meeting the beach at an oblique angle, and back washing perpendicular to the shore, moving sediment down the beach in a zigzag pattern. Longshore drifting is complemented by longshore currents, which transport sediment through the water alongside the beach. These currents are set in motion by the same oblique angle of entering waves that cause littoral drift and transport sediment in a similar process. The hydrodynamic interaction between the longshore current and water inflow from the Terengganu Mouth River is causing the changes in spit's geomorphology characteristics. This finding confirms the study of Marghany et al., (2010a) ; Marghany et al., (2010b) and Marghany (2011). The increasing growth of spit across the estuary is due to impact of sedimentation due to littoral drift. According to Marghany and Mazlan (2010a) net littoral drift along Kuala Terengganu coastal water is towards the southward which could induce the growth of spit length.

### Fig. 6. DEM of coastal spit.

Finally, a difference statistical comparison confirms the results of Figs 4,5 and 6. Table 2 shows the statistical comparison between the simulated DEM from the DInSAR, real ground measurements and with using fuzzy B-spline. This table represents the bias (averages mean the standard error, 90 and 95% confidence intervals, respectively. Evidently, the DInSAR

Simulation of 3-D Coastal Spit Geomorphology

Systems, 72,123-156.

*Plan. Sci.* 28: 169–209.

Academic, Dordrecht, Boston.

2,11767–1771.

23.

3,187 – 206.

decorrelation.

**7. References** 

1550.

Using Differential Synthetic Aperture Interferometry (DInSAR) 93

interfeorgram using conventional DInSAR because of temporal decorrelation. The result shows that spit and vegetation zone have poor coherence of 0.25 as compared to the urban area. In addition, only small portion of the F1 mode scene was processed because of temporal decorrelation. Finally, the fuzzy B-spline algorithm used to reconstruct fringe pattern, and 3-D from decorrelate unwrap phase. The fringe pattern shows the deformation of 0.4 cm along spit and 1.4 cm in urban area. Further, the maximum 3-D spit elevation is 3 m with the standard error of mean of ± 0.034 m. In conclusion, the integration between the conventional DInSAR method and the FBSs could be an excellent tool for 3-D coastal geomorphology reconstruction from SAR data the under circumstance of temporal

Anile, A.M., B. Falcidieno, G. Gallo, M. Spagnuolo, S. Spinello, (2000). "Modeling uncertain

Anile, AM, Deodato, S, Privitera, G, (1995) *Implementing fuzzy arithmetic*, Fuzzy Sets and

Askne, J., M. Santoro, G. Smith, and J. E. S. Fransson (2003). "Multitemporal repeat-pass

Burgmann, R., P.A. Rosen, and E.J. Fielding (2000). "Synthetic aperture radar interferometry

Fuchs, H. Z.M. Kedem, and Uselton, S.P., (1977). Optimal Surface Reconstruction from

Gens,R., (2000)."The influence of input parameters on SAR interferometric processing and

Hanssen R.F., (2001). *Radar Interferometry: Data Interpretation and Error Analysis*, Kluwer

Lee H., (2001). "Interferometric Synthetic Aperture Radar Coherence Imagery for Land

Luo, X., F.Huang, and G. Liu, (2006). "Extraction co-seismic Deformation of Bam

Massonnet, D. and K. L. Feigl (1998).,"Radar interferometry and its application to changes in

Marghany M (2012). 3-D Coastal Bathymetry Simulation from Airborne TOPSAR Polarized

Marghany M (2011).Three-dimensional visualisation of coastal geomorphology using fuzzy B-spline of dinsar technique. Int. J. of the Phys. Sci. 6(30):6967 – 6971. Marghany,M., M. Hashim and A. P. Cracknell, (2010a)."3-D visualizations of coastal

Surface Change Detection" Ph.D theses, University of London.

the earth's surface,"*Rev. Geophys.* 36, 441–500 .

Publisher, University Campus STeP Ri, Croatia, 57-76.

SAR interferometry of boreal forests," *IEEE Trans. Geosci. Remote Sens.* 41, 1540–

to measure Earth's surface topography and its deformation", *Ann. Rev.of Earth and* 

its implication on the calibration of SAR interferometric data", *Int. J. Remote Sens.*

earthquake with Differential SAR Interferometry". *J. New Zea. Inst. of Surv*. 296:20-

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data with fuzzy B-splines", Fuzzy Sets and Syst. 113, 397-410.

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using fuzzy B-spline performance has bias of-0.05 m, lower than ground measurements and the DInSAR method. Therefore, fuzzy B-spline has a standard error of mean of ± 0.034 m, lower than ground measurements and the DInSAR method. Overall performances of DInSAR method using fuzzy B-spline is better than DInSAR technique which is validated by a lower range of error (0.02±0.21 m) with 90% confidence intervals.


Table 2. Statistical Comparison between DInSAR and DInSAR-Fuzzy B-spline Techniques.

Fuzzy B-spline produced perfect pattern of fringe interfeormetry compared with one produced by DInSAR technique (Fig. 5). It shows there are many deformations of over several centimetres. In these deformations, it is known the deformation in spit because of coastline sedimentation. The other deformations, however, are caused not by the movement of the coastal sediment but the spatial fluctuation of water vapour in the atmosphere. In addition, the growths of urban area induces also land cover changes. Further, it can be noticed that fuzzy B-spline preserves detailed edges with discernible fringes (Russo 1998 and Rövid et al. 2004). Indeed, Fig 5. shows smooth interferogram, in terms of spatial resolution maintenance, and noise reduction, compared to conventional methods (Zebker et al.,1997; Massonnet, and Feigl 1998; Burgmann et al., 2000; Hanssen 2001; Yang et al., 2007; Rao and Jassar (2010).

This has been contributed since each operation on a fuzzy number becomes a sequence of corresponding operations on the respective μ -levels , and the multiple occurrences of the same fuzzy parameters evaluated because of the function on fuzzy variables (Anile et L., 1995 and Anile et al., 2000). It is easy to distinguish between small and long fringes. Typically, in computer graphics, two objective quality definitions for fuzzy B-spline were used: triangle-based criteria and edge-based criteria. Triangle-based criteria follow the rule of maximization or minimization, respectively, of the angles of each triangle (Fuchs et al. 1997). The so-called max-min angle criterion prefers short triangles with obtuse angles. This result agrees confirms the studies of Anile et al. (2000); Marghany et al.,(2010a); and Marghany (2011).

### **6. Conclusions**

Synthetic Aperture Radar interferometry (InSAR) is a relatively new technique for 3-D topography mapping. This study presents a new approach for 3-D object simulation using Differential synthetic aperture interferometry (DInSAR). This work has demonstrated the 3- D spit reconstruction from DInSAR using three C-band SAR images acquired by RADARSAT-1 SAR F 1 mode data. The conventional method of DInSAR used to create 3-D coastal geomorphology reconstruction. Nevertheless, it was difficult to generate phase and interfeorgram using conventional DInSAR because of temporal decorrelation. The result shows that spit and vegetation zone have poor coherence of 0.25 as compared to the urban area. In addition, only small portion of the F1 mode scene was processed because of temporal decorrelation. Finally, the fuzzy B-spline algorithm used to reconstruct fringe pattern, and 3-D from decorrelate unwrap phase. The fringe pattern shows the deformation of 0.4 cm along spit and 1.4 cm in urban area. Further, the maximum 3-D spit elevation is 3 m with the standard error of mean of ± 0.034 m. In conclusion, the integration between the conventional DInSAR method and the FBSs could be an excellent tool for 3-D coastal geomorphology reconstruction from SAR data the under circumstance of temporal decorrelation.

### **7. References**

92 Recent Interferometry Applications in Topography and Astronomy

using fuzzy B-spline performance has bias of-0.05 m, lower than ground measurements and the DInSAR method. Therefore, fuzzy B-spline has a standard error of mean of ± 0.034 m, lower than ground measurements and the DInSAR method. Overall performances of DInSAR method using fuzzy B-spline is better than DInSAR technique which is validated by

**DInSAR DInSAR-Fuzzy B-spline**

 2.5 -0.05 1.5 0.034

 **Lower Upper Lower Upper**  1.2 2.6 0.02 0.16

a lower range of error (0.02±0.21 m) with 90% confidence intervals.

**Bias** 

**Standard error of the mean**

Rao and Jassar (2010).

Marghany (2011).

**6. Conclusions** 

**90 % (90 % confidence interval )** 

**Statistical Parameters DInSAR techniques**

**95 % (95 % confidence interval )** 0.98 2.35 0.03 0.21

Table 2. Statistical Comparison between DInSAR and DInSAR-Fuzzy B-spline Techniques.

Fuzzy B-spline produced perfect pattern of fringe interfeormetry compared with one produced by DInSAR technique (Fig. 5). It shows there are many deformations of over several centimetres. In these deformations, it is known the deformation in spit because of coastline sedimentation. The other deformations, however, are caused not by the movement of the coastal sediment but the spatial fluctuation of water vapour in the atmosphere. In addition, the growths of urban area induces also land cover changes. Further, it can be noticed that fuzzy B-spline preserves detailed edges with discernible fringes (Russo 1998 and Rövid et al. 2004). Indeed, Fig 5. shows smooth interferogram, in terms of spatial resolution maintenance, and noise reduction, compared to conventional methods (Zebker et al.,1997; Massonnet, and Feigl 1998; Burgmann et al., 2000; Hanssen 2001; Yang et al., 2007;

This has been contributed since each operation on a fuzzy number becomes a sequence of corresponding operations on the respective μ -levels , and the multiple occurrences of the same fuzzy parameters evaluated because of the function on fuzzy variables (Anile et L., 1995 and Anile et al., 2000). It is easy to distinguish between small and long fringes. Typically, in computer graphics, two objective quality definitions for fuzzy B-spline were used: triangle-based criteria and edge-based criteria. Triangle-based criteria follow the rule of maximization or minimization, respectively, of the angles of each triangle (Fuchs et al. 1997). The so-called max-min angle criterion prefers short triangles with obtuse angles. This result agrees confirms the studies of Anile et al. (2000); Marghany et al.,(2010a); and

Synthetic Aperture Radar interferometry (InSAR) is a relatively new technique for 3-D topography mapping. This study presents a new approach for 3-D object simulation using Differential synthetic aperture interferometry (DInSAR). This work has demonstrated the 3- D spit reconstruction from DInSAR using three C-band SAR images acquired by RADARSAT-1 SAR F 1 mode data. The conventional method of DInSAR used to create 3-D coastal geomorphology reconstruction. Nevertheless, it was difficult to generate phase and


**0**

**5**

*Japan*

**Local, Fine Co-Registration of SAR Interferometry**

*Department of Electrical Engineering and Information Systems, The University of Tokyo*

Synthetic aperture radar (SAR) has great advantage of being able to observe large area accurately in any weather. It can measure various properties of the earth Boerner (2003), e.g., the topography, the vegetation Hajinsek et al. (2009), and the landscape changes caused by earthquakes or volcanoes Gabriel et al. (1989). One of the common usages of SAR is Interferometric synthetic aperture radar (InSAR), which can measure the landscape with an interferogram of SAR images. The SAR interferogram is made from two complex-valued maps obtained by observing identical place, named "master" and "slave." The phase information of the interferogram corresponds to the ground topography. To generate digital elevation model (DEM) from interferogram, phase unwrapping process is required. However, an unwrapping process is disturbed seriously by singular points (SPs), the rotational points

Most of the SPs hinder us from creating accurate DEM Ghiglia & Pritt (1998). Many researchers have tried to solve this problem by proposing novel methods concerning branch-cut techniques Costantini (1998), least squares Pritt & Shipman (1994), and singularity spreading technique Yamaki & Hirose (2007). These major methods have numerous efficient improvements e.g., Fornaro et al. (1996) Reigber & Moreia (1997) Suksmono & Hirose (2006). Various SP elimination filters have also developed and applied to the interferogram. For example, Lee filter Lee et al. (1998), Goldstein filter Goldstein & Werner (1998), Bayesian filter Ferraiuolo & Poggi (2004), and Markov random field modeled filter Suksmono & Hirose

There are three origins in the SP generation. One is the low SNR caused by low scattering reflectance. Another one is the sharp cliff and layover. The landscape can be so rough that the aliasing occurs. The last one is the local distortion in the co-registration of the master and the slave. That is, the reflection, scattering and fore-shortening can be different in the two observations with slightly different sight angle, resulting in local phase distortion in the interferogram. Filtering and unwrapping methods can solve first two origins. On the other

**1. Introduction**

existing in the phase map.

(2002) Yamaki & Hirose (2009) are the popular.

hand, the last origin, the local distortion, has been generally ignored.

**Using the Number of Singular Points**

**for the Evaluation**

Ryo Natsuaki and Akira Hirose


## **Local, Fine Co-Registration of SAR Interferometry Using the Number of Singular Points for the Evaluation**

Ryo Natsuaki and Akira Hirose *Department of Electrical Engineering and Information Systems, The University of Tokyo Japan*

### **1. Introduction**

94 Recent Interferometry Applications in Topography and Astronomy

Marghany, M., and M. Hashim (2009)."Differential Synthetic Aperture radar Interferometry

Marghany, M., and M. Hashim (2010a)."Different polarised topographic synthetic aperture

Marghany, M.,Z. Sabu and M. Hashim,(2010b) "Mapping coastal geomorphology changes

Marghany M., and M. Hashim (2010b). "Velocity bunching and Canny algorithms for

Nizalapur, V., R. Madugundu, and C. Shekhar Jha (2011). "Coherence-based land cover

RADARSAT International, (2011)"RADARSAT application [online] Available from

Rao, K.S., H. K. Al Jassar, S. Phalke, Y. S. Rao, J. P. Muller, and. Z. Li, (2006). "A study on

Rao, K.S.,and H. K. Al Jassar (2010). "Error analysis in the digital elevation model of Kuwait

Russo, F., (1998).Recent advances in fuzzy techniques for image enhancement. IEEE Transactions on Instrumentation and measurement. 47, pp: 1428-1434. Rövid, A., Várkonyi, A.R. andVárlaki, P., (2004). 3D Model estimation from multiple

Yang, J., T.Xiong, and Y. Peng, (2007). "A fuzzy Approach to Filtering Interferometric SAR

Zebker, H.A., C.L.,Werner, P.A. Rosen, and S. Hensley, (1994). "Accuracy of Topographic

Zebker, H.A., P.A. Rosen, and S. Hensley (1997)."Atmospheric effects in inteferometric

using synthetic aperture radar data". *Int. J. Phys. Sci. 5,*1890-1896.

Sci. and Network Secu., 9,59-63.

http:\www.rsi.ca [Accessed 8 June 2011].

several Indian test sites," *Int. J. Remote Sens.* 27, 595–616.

25-29, 2004, Budapest, Hungary, pp. 1661-1666.

Data". *Int. J. of Remote Sens.*, 28, 1375-1382.

*Sci. 5,*1908-1914.

*Appl.Remote Sens*.4,1-24.

059501-6.

836.

*Res.*102, 7547–7563.

(DInSAR) for 3D Coastal Geomorphology Reconstruction". IJCSNS Int. J. of Comp.

radar (TOPSAR) bands for shoreline change mapping. *Int. J. Phys. Sci. 5*, 1883-1889.

modelling shoreline change rate from synthetic aperture radar (SAR). *Int. J. Phys.* 

classification in forested areas of Chattisgarh, Central India, using environmental satellite—advanced synthetic aperture radar data", *J. Appl.Remote Sens.* 5, 059501-1-

the applicability of repeat pass SAR interferometry for generating DEMs over

desert derived from repeat pass synthetic aperture radar interferometry", *J.* 

images," IEEE International Conference on Fuzzy Systems, FUZZ-IEEE'2004, July

Maps Derived from ERS-1 Interferometric Radar", *IEEE Geosci. Remote Sens.,*2,823-

synthetic aperture radar surface deformation and topographic maps", *J. Geophys.* 

Synthetic aperture radar (SAR) has great advantage of being able to observe large area accurately in any weather. It can measure various properties of the earth Boerner (2003), e.g., the topography, the vegetation Hajinsek et al. (2009), and the landscape changes caused by earthquakes or volcanoes Gabriel et al. (1989). One of the common usages of SAR is Interferometric synthetic aperture radar (InSAR), which can measure the landscape with an interferogram of SAR images. The SAR interferogram is made from two complex-valued maps obtained by observing identical place, named "master" and "slave." The phase information of the interferogram corresponds to the ground topography. To generate digital elevation model (DEM) from interferogram, phase unwrapping process is required. However, an unwrapping process is disturbed seriously by singular points (SPs), the rotational points existing in the phase map.

Most of the SPs hinder us from creating accurate DEM Ghiglia & Pritt (1998). Many researchers have tried to solve this problem by proposing novel methods concerning branch-cut techniques Costantini (1998), least squares Pritt & Shipman (1994), and singularity spreading technique Yamaki & Hirose (2007). These major methods have numerous efficient improvements e.g., Fornaro et al. (1996) Reigber & Moreia (1997) Suksmono & Hirose (2006). Various SP elimination filters have also developed and applied to the interferogram. For example, Lee filter Lee et al. (1998), Goldstein filter Goldstein & Werner (1998), Bayesian filter Ferraiuolo & Poggi (2004), and Markov random field modeled filter Suksmono & Hirose (2002) Yamaki & Hirose (2009) are the popular.

There are three origins in the SP generation. One is the low SNR caused by low scattering reflectance. Another one is the sharp cliff and layover. The landscape can be so rough that the aliasing occurs. The last one is the local distortion in the co-registration of the master and the slave. That is, the reflection, scattering and fore-shortening can be different in the two observations with slightly different sight angle, resulting in local phase distortion in the interferogram. Filtering and unwrapping methods can solve first two origins. On the other hand, the last origin, the local distortion, has been generally ignored.

The phase value Φ of the interferogram corresponds to *Rm* and *Rs* as

From (1) and (2), the relationship between Φ and *θ* is expressed as

*λ*Φ

ΔΦ

height increment of the observation point Δ*H* can be expressed as

If there is a height increment between the neighbor pixels, the increment of Φ is

Δ*H*

<sup>Δ</sup>*<sup>H</sup>* <sup>=</sup> *<sup>λ</sup>Rm* sin(*θ*)

 *c*

unwrapping will fail. We assume that there are three origins of the SP emergence.

3. Local distortion in the co-registration of the master and the slave

1. Low SNR caused by low scattering reflectance

2. Sharp cliff and layover

<sup>Δ</sup>*<sup>θ</sup>* <sup>=</sup> <sup>4</sup>*πBCT* cos(*<sup>θ</sup>* <sup>−</sup> *<sup>γ</sup>CT*)

<sup>97</sup> Local, Fine Co-Registration of SAR Interferometry

From (4) and (5), the relationship between the interferogram phase increment ΔΦ and the

4*πBCT* cos(*θ* − *γCT*)

which indicates that the phase gradient of 2*π* corresponds to the height gradient of

In order to analyze the ground topography, we have to unwrap, line integrate, the phase information. As the ground topography is the conservative field, its contour integral should

However, there are many non-zero rotational points, namely singular points (SPs), in the interferogram. As shown in Fig.2, if there is a rotational point in the interferogram, phase

Origin (i) is generally thought as the main reason of SPs which should be erased. SPs generated by origin (ii) should remain. The third reason (iii) has been conventionally ignored. A pixel in the master representing a small local area should completely correspond to a pixel in the slave that represents the same area. However, we assume that the slight difference of the radar incidence direction between the master and the slave distorts this correspondence

Geometrically, *Rm* − *Rs* corresponds to *BCT* and *γCT* as

Using the Number of Singular Points for the Evaluation

and the increment of *H* is

*λRm* sin(*θ*) <sup>2</sup>*BCT* cos(*θ*−*γCT*).

be zero.

*λ*Φ

<sup>2</sup>*<sup>π</sup>* <sup>=</sup> <sup>2</sup> (*Rm* <sup>−</sup> *Rs*) (1)

(*Rm* − *Rs*) = *BCT* sin (*θ* − *γCT*) (2)

<sup>2</sup>*<sup>π</sup>* <sup>=</sup> <sup>2</sup>*BCT* sin (*<sup>θ</sup>* <sup>−</sup> *<sup>γ</sup>CT*) (3)

<sup>Δ</sup>*<sup>θ</sup>* <sup>=</sup> *Rm* sin(*θ*) (5)

ΔΦ*ds*� = 0 (7)

*<sup>λ</sup>* (4)

ΔΦ (6)

Without the distortion, no SP is expected through an appropriate co-registration of non-aliasing master and slave maps. Usually the co-registration is realized by maximizing the amplitude cross-correlation of the maps in macro scale, while by maximizing the complex-amplitude correlation in micro scale. The correlations require an averaging process over a certain area for sufficient reduction of included noise. However, a wide-area averaging degrades the locality in the matching required to eliminate the distortion. This trade-off brings a limitation in the co-registration performance. In short, the difference in the reflection, scattering and fore-shortening yields local distortion, and SPs are generated inevitably by the cross-correlation process.

In this chapter, we firstly introduce the basis of InSAR and its SP problem. Secondly, we introduce a local and fine co-registration method which employs the number of SPs as evaluation criterion (SPEC method Natsuaki & Hirose (2011)). Finally, we demonstrate the effectiveness of the improvement by comparing the DEMs generated from interferograms which co-registered with and without the SPEC method. For experiment, we use the data of Mt. Fuji observed by JERS-1 which was launched by JAXA (Japan Aerospace Exploration Agency). Mt. Fuji has an ordinary single volcanic cone shape.

### **2. InSAR and SP problem**

Fig. 1. Schematic diagram of InSAR

Figure 1 shows the observation system of InSAR. We define wave length as *λ*, elevation angle as *θ*, distances from ground to the master and the slave satellite as *Rm* and *Rs*, distance between the master and the slave as *BCT*, relative angle of the master and the slave as *γCT*. The phase value Φ of the interferogram corresponds to *Rm* and *Rs* as

$$\frac{\lambda\Phi}{2\pi} = 2\left(R\_{\text{fl}} - R\_{\text{s}}\right) \tag{1}$$

Geometrically, *Rm* − *Rs* corresponds to *BCT* and *γCT* as

$$(R\_{\mathfrak{m}} - R\_{\mathfrak{s}}) = B\_{\text{CT}} \sin \left( \theta - \gamma\_{\text{CT}} \right) \tag{2}$$

From (1) and (2), the relationship between Φ and *θ* is expressed as

$$\frac{\lambda\Phi}{2\pi} = 2B\_{CT}\sin\left(\theta - \gamma\_{CT}\right) \tag{3}$$

If there is a height increment between the neighbor pixels, the increment of Φ is

$$\frac{\Delta\Phi}{\Delta\theta} = \frac{4\pi B\_{\text{CT}}\cos(\theta - \gamma\_{\text{CT}})}{\lambda} \tag{4}$$

and the increment of *H* is

$$\frac{\Delta H}{\Delta \theta} = R\_m \sin(\theta) \tag{5}$$

From (4) and (5), the relationship between the interferogram phase increment ΔΦ and the height increment of the observation point Δ*H* can be expressed as

$$
\Delta H = \frac{\lambda R\_m \sin(\theta)}{4\pi B\_{\rm CT} \cos(\theta - \gamma\_{\rm CT})} \Delta \Phi \tag{6}
$$

which indicates that the phase gradient of 2*π* corresponds to the height gradient of *λRm* sin(*θ*)

<sup>2</sup>*BCT* cos(*θ*−*γCT*).

2 Will-be-set-by-IN-TECH

Without the distortion, no SP is expected through an appropriate co-registration of non-aliasing master and slave maps. Usually the co-registration is realized by maximizing the amplitude cross-correlation of the maps in macro scale, while by maximizing the complex-amplitude correlation in micro scale. The correlations require an averaging process over a certain area for sufficient reduction of included noise. However, a wide-area averaging degrades the locality in the matching required to eliminate the distortion. This trade-off brings a limitation in the co-registration performance. In short, the difference in the reflection, scattering and fore-shortening yields local distortion, and SPs are generated inevitably by the

In this chapter, we firstly introduce the basis of InSAR and its SP problem. Secondly, we introduce a local and fine co-registration method which employs the number of SPs as evaluation criterion (SPEC method Natsuaki & Hirose (2011)). Finally, we demonstrate the effectiveness of the improvement by comparing the DEMs generated from interferograms which co-registered with and without the SPEC method. For experiment, we use the data of Mt. Fuji observed by JERS-1 which was launched by JAXA (Japan Aerospace Exploration

Ground Range

θ

*H*

Agency). Mt. Fuji has an ordinary single volcanic cone shape.

Slave

*Rm*

Land surface

*Rs*

Figure 1 shows the observation system of InSAR. We define wave length as *λ*, elevation angle as *θ*, distances from ground to the master and the slave satellite as *Rm* and *Rs*, distance between the master and the slave as *BCT*, relative angle of the master and the slave as *γCT*.

cross-correlation process.

**2. InSAR and SP problem**

Height

Fig. 1. Schematic diagram of InSAR

Master

γ*CT*

*BCT*

In order to analyze the ground topography, we have to unwrap, line integrate, the phase information. As the ground topography is the conservative field, its contour integral should be zero.

$$\oint\_{\varepsilon} \Delta \Phi ds' = 0 \tag{7}$$

However, there are many non-zero rotational points, namely singular points (SPs), in the interferogram. As shown in Fig.2, if there is a rotational point in the interferogram, phase unwrapping will fail. We assume that there are three origins of the SP emergence.


Origin (i) is generally thought as the main reason of SPs which should be erased. SPs generated by origin (ii) should remain. The third reason (iii) has been conventionally ignored. A pixel in the master representing a small local area should completely correspond to a pixel in the slave that represents the same area. However, we assume that the slight difference of the radar incidence direction between the master and the slave distorts this correspondence

left *8/8* Left most

Using the Number of Singular Points for the Evaluation

left *8/8*

right *1/8*

Slave Master Slave leftward rightward

<sup>99</sup> Local, Fine Co-Registration of SAR Interferometry

right *1/8*

right *2/8*

right *3/8*

right *4/8*

right *5/8*

right *6/8*

right *7/8*

right *8/8*

right *2/8*

right *3/8*

right *4/8*

right *5/8*

right *6/8*

right *7/8*

right *8/8*

left *7/8*

left *6/8*

left *5/8*

left *4/8*

left *3/8*

left *2/8*

left *1/8*

Center

Fig. 4. Interferograms and SP plots obtained by moving the slave map from the position of maximum cross correlation leftward or rightward by integral multiple of 1/8 subpixels for

Center *0/8*

left *7/8*

left *6/8*

left *5/8*

left *4/8*

left *3/8*

left *2/8*

left *1/8*

*0/8*

the area of the right half of the black square in Fig.3(a).

Right most

Fig. 2. Failure of unwrapping due to the existence of the SP.

in sub-pixel order, and that interferograms show these local distortions as massive SPs. In the next section, we introduce the local-o-registration method to solve the local distortion.

### **3. Singular points as evaluation criterion**

**3.1 Typical co-registration technique and the changes of SP distributions with subpixel shifts**

(a) (b) Fig. 3. (a)Interferogram of Mt. Fuji (black square corresponds to Fig.8.) and (b)its SP plot made by the typical method (# SPs = 11,518).

To create an interferogram with master and slave, we have to co-register them in advance as they observe the same place from slightly different angle. The typical co-registration process is explained as follows Tobita et al. (1999). First, we affine-transform the slave map adaptively to maximize the cross correlation between the master and slave amplitude maps in a macro scale, e.g., 64×64 pixels. Next, we maximize the complex-valued cross correlation locally in 1/32 subpixels with interpolation, e.g., 8×8 pixels. Figure 3(a) shows the interferogram of Mt. Fuji created by this method, and Fig.3(b) gives its SP plot. This interferogram has 304×304 pixels and contains 11,518 SPs. In Fig.3(a), the phase value is shown in gray scale, in which a white dot stands for *π* as the phase value and a black dot means −*π*. In all figures in this article, the up-down direction is the azimuth and the left-right direction is the range. In Fig.3(b), a white dot indicates a clockwise SP, while a black dot shows a counterclockwise one. 4 Will-be-set-by-IN-TECH

in sub-pixel order, and that interferograms show these local distortions as massive SPs. In the next section, we introduce the local-o-registration method to solve the local distortion.

**3.1 Typical co-registration technique and the changes of SP distributions with subpixel**

π

Position *m*

50 100 150 200 250 300 Position *n*

−2π

2π

*0*

*0*

−π

(b) Fig. 3. (a)Interferogram of Mt. Fuji (black square corresponds to Fig.8.) and (b)its SP plot

To create an interferogram with master and slave, we have to co-register them in advance as they observe the same place from slightly different angle. The typical co-registration process is explained as follows Tobita et al. (1999). First, we affine-transform the slave map adaptively to maximize the cross correlation between the master and slave amplitude maps in a macro scale, e.g., 64×64 pixels. Next, we maximize the complex-valued cross correlation locally in 1/32 subpixels with interpolation, e.g., 8×8 pixels. Figure 3(a) shows the interferogram of Mt. Fuji created by this method, and Fig.3(b) gives its SP plot. This interferogram has 304×304 pixels and contains 11,518 SPs. In Fig.3(a), the phase value is shown in gray scale, in which a white dot stands for *π* as the phase value and a black dot means −*π*. In all figures in this article, the up-down direction is the azimuth and the left-right direction is the range. In Fig.3(b), a white dot indicates a clockwise SP, while a black dot shows a counterclockwise one.

π

−π

**3. Singular points as evaluation criterion**

**shifts**

Position *m*

Fig. 2. Failure of unwrapping due to the existence of the SP.

50 100 150 200 250 300 Position *n*

(a)

made by the typical method (# SPs = 11,518).

Fig. 4. Interferograms and SP plots obtained by moving the slave map from the position of maximum cross correlation leftward or rightward by integral multiple of 1/8 subpixels for the area of the right half of the black square in Fig.3(a).

(b)

*S/8(m,n)*

*S/8(m, n+1)*

*S/8(p,q; m,n)*

*S/8(m+1 ,n+1)*

*S/8(m+1 ,n)*

master

master

slave

slave

16

16

64 16

64

64 16

64

Fig. 6. Relationship between the blocks and the interferogram pixels: (a)Blocks for making regular 16-look mean-filtered interferogram in 1 pixel coordinate system, (b)blocks equal to (a) in 1/8-pixel coordinate system, (c)a SP in the interferogram made in 1/8-pixel coordinate

16 (=8×2) interferogram pixels. That is, to make an interferogram, in this paper, 8 times azimuth compression and 2 times range compression are required (i.e., to make a 304×304 pixels interferogram, 2432×608 pixels master and slave are required). Next, we find SPs in it and co-register interpolated master with interpolated slave locally and nonlinearly as follows.

Figures 6 and 7 are schematic diagrams of our local and nonlinear co-registration based on the number of SPs. We call the 8-times interpolated master and slave maps as "1/8-pixel

**3.3 Details of the local and nonlinear co-registration based on the number of SPs**

system, and (d)local movement of the interpolated slave to delete the SP.

(d)

*S/8(m,n)*

*new*

*S/8(m, n+1)*

*S/8(1,1; m,n) S/8(1,1; m,n)*

*new*

*S/8(m+1 ,n+1)*

*S/8(m+1 ,n)*

(c)

*+1*

*I/8(m, n+1)*

*I/8(m+1 ,n+1)*

*I/8(m,n)*

*I/8(m+1 ,n)*

(a)

*S(m,n)*

Using the Number of Singular Points for the Evaluation

*S(m, n+1)*

*S(p,q; m,n)*

*S(m+1 ,n+1)*

*S(m+1 ,n)*

master

Interferogram

slave

<sup>101</sup> Local, Fine Co-Registration of SAR Interferometry

2

8 2

8

1

1

Figure 4 represents how the interferogram and its SP plot change when the slave shifts leftward or rightward by integral multiple of 1/8 pixel from the maximum cross-correlation position for the right half area in the black square in Fig.3(a). It is obvious that many SPs move, emerge, or disappear, but the fringes in the interferogram show only small changes.

The emergence and the disappearance occur rather locally than the scale of correlation calculation. This fact suggests that we need a more local, and consequently nonlinear, co-registration process in addition to the conventional one. The changes in the fringes is not so large, which means that the rough landscape is not changed by this additional process, but the local precise co-registration is expected to improve the local landscape since, basically, no SPs are expected in non-distorted interferogram.

The aim of our proposal is to improve the accuracy of DEM by removing the local distortion. In this removal process, we pay attention to the number of SPs as explained in the following section. Based on this idea which came from the result of the above preliminary experiment, we introduce our new method below.

### **3.2 Proposal of the SPEC method**

Fig. 5. Flowchart of the whole co-registration process including the SPEC method.

Figure 5 is the flowchart of the whole co-registration process including our SPEC method. First, we co-register master *M* and slave *S* by the conventional method as explained in Section 3.1. Then we make an interferogram *I* from master *M* and slave *S* with 16-look mean-filtering as

$$I(m,n) = \frac{1}{16} \sum\_{q=1}^{8} \sum\_{p=1}^{2} M(p,q;m,n) \mathcal{S}^\*(p,q;m,n). \tag{8}$$

Fig. 6(a) explains the process. We regard the 8×2 pixels in the master and the slave as single blocks, **M**(*m*, *n*) and **S**(*m*, *n*), respectively, each of which pair yields one pixel in 16-look interferogram shown in Fig. 6(a). *M*(*p*, *q*; *m*, *n*) represents the *p*-th top and *q*-th left pixel in the block **M**(*m*, *n*). The 16-look mean-filtering works to decrease the noise by averaging 6 Will-be-set-by-IN-TECH

Figure 4 represents how the interferogram and its SP plot change when the slave shifts leftward or rightward by integral multiple of 1/8 pixel from the maximum cross-correlation position for the right half area in the black square in Fig.3(a). It is obvious that many SPs move, emerge, or disappear, but the fringes in the interferogram show only small changes. The emergence and the disappearance occur rather locally than the scale of correlation calculation. This fact suggests that we need a more local, and consequently nonlinear, co-registration process in addition to the conventional one. The changes in the fringes is not so large, which means that the rough landscape is not changed by this additional process, but the local precise co-registration is expected to improve the local landscape since, basically, no

The aim of our proposal is to improve the accuracy of DEM by removing the local distortion. In this removal process, we pay attention to the number of SPs as explained in the following section. Based on this idea which came from the result of the above preliminary experiment,

Interferogram(original)

Macro Registration

16Look Mean Filter

Master, Slave (Original)

Interferogram(new)

Phase Unwrapping

Digital Elevation Model

Fig. 5. Flowchart of the whole co-registration process including the SPEC method.

*<sup>I</sup>*(*m*, *<sup>n</sup>*) = <sup>1</sup>

16

8 ∑ *q*=1

2 ∑ *p*=1

Figure 5 is the flowchart of the whole co-registration process including our SPEC method. First, we co-register master *M* and slave *S* by the conventional method as explained in Section 3.1. Then we make an interferogram *I* from master *M* and slave *S* with 16-look mean-filtering

Fig. 6(a) explains the process. We regard the 8×2 pixels in the master and the slave as single blocks, **M**(*m*, *n*) and **S**(*m*, *n*), respectively, each of which pair yields one pixel in 16-look interferogram shown in Fig. 6(a). *M*(*p*, *q*; *m*, *n*) represents the *p*-th top and *q*-th left pixel in the block **M**(*m*, *n*). The 16-look mean-filtering works to decrease the noise by averaging

1024Look Mean Filter

*M*(*p*, *q*; *m*, *n*)*S*∗(*p*, *q*; *m*, *n*). (8)

Local Registration

Master, Slave (8x Interpolated)

Interpolation

Section 3.3 (details)

SP detection

SPs are expected in non-distorted interferogram.

we introduce our new method below.

**3.2 Proposal of the SPEC method**

Section 3.1

Section 3.2 [The SPEC]

as

Fig. 6. Relationship between the blocks and the interferogram pixels: (a)Blocks for making regular 16-look mean-filtered interferogram in 1 pixel coordinate system, (b)blocks equal to (a) in 1/8-pixel coordinate system, (c)a SP in the interferogram made in 1/8-pixel coordinate system, and (d)local movement of the interpolated slave to delete the SP.

16 (=8×2) interferogram pixels. That is, to make an interferogram, in this paper, 8 times azimuth compression and 2 times range compression are required (i.e., to make a 304×304 pixels interferogram, 2432×608 pixels master and slave are required). Next, we find SPs in it and co-register interpolated master with interpolated slave locally and nonlinearly as follows.

### **3.3 Details of the local and nonlinear co-registration based on the number of SPs**

Figures 6 and 7 are schematic diagrams of our local and nonlinear co-registration based on the number of SPs. We call the 8-times interpolated master and slave maps as "1/8-pixel

Map Status Notation Unit

<sup>103</sup> Local, Fine Co-Registration of SAR Interferometry

in 8-times interpolation *I*/8(*m*, *n*)

We first make an 1/8-pixel coordinate-system interferogram locally. The pixel value *I*/8(*m*, *n*), which corresponds to a pixel of a 16-look mean-filtered interferogram *I*(*m*, *n*), is calculated as

where *M*/8(*p*, *q*; *m*, *n*) represents the *p*-th top and *q*-th left pixel in the block **M**/8(*m*, *n*), while *S*/8(*p*, *q*; *m*, *n*) represents the *p*-th and *q*-th pixel in **S**/8(*m*, *n*) in the same manner. For example, if there is a SP at *I*/8(*m*, *n*), *I*/8(*m* + 1, *n*), *I*/8(*m*, *n* + 1), *I*/8(*m* + 1, *n* + 1) in the interferogram,

Simultaneously, in this square *I*/8(*m*, *n*)—*I*/8(*m* + 1, *n* + 1), there is local distortion in the master and / or the slave. Then we therefore move one or some of the blocks among the four **S**/8(*m*, *n*)—**S**/8(*m* + 1, *n* + 1) blocks to modify the interferogram. For example, we move

/8 (1, 16; *m*, *n*)

/8 (2, 16; *m*, *n*)

. .

/8 (64, 16; *m*, *n*)

*θ*/8(*m*, *n*) − *θ*/8(*m*, *n* + 1)

*M*/8(*p*, *q*; *m*, *n*)*S*<sup>∗</sup>

*M*(*p*, *q*; *m*, *n*)

**M**(*m*, *n*)

*M*/8(*p*, *q*; *m*, *n*)

**M**/8(*m*, *n*)

� +

*θ*/8(*m*, *n*) ≡ arg(*I*/8(*m*, *n*)). (11)

/8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* + 1, *q* + 1; *m*, *n*) to try to erase

⎞

⎟⎟⎟⎟⎟⎟⎟⎠

*θ*/8(*m* + 1, *n* + 1) − *θ*/8(*m*, *n* + 1)

*S*(*p*, *q*; *m*, *n*) pixel

**S**(*m*, *n*) block

*S*/8(*p*, *q*; *m*, *n*) subpixel

**S**/8(*m*, *n*) block

mean-filtered pixel

mean-filtered pixel

/8(*p*, *q*; *m*, *n*) (9)

��

� ≥ 2*π* (10)

interferogram 16-look mean-filtered *I*(*m*, *n*)

master, slave single look

in master, slave single look

*<sup>I</sup>*/8(*m*, *<sup>n</sup>*) = <sup>1</sup>

as shown in Fig.6(c), we find non-zero rotation as

*θ*/8(*m* + 1, *n* + 1) − *θ*/8(*m* + 1, *n*)

**S**/8(*m*, *n*) locally in such a manner that *S*new

/8 (1, 1; *<sup>m</sup>*, *<sup>n</sup>*) *<sup>S</sup>*new

/8 (2, 1; *<sup>m</sup>*, *<sup>n</sup>*) *<sup>S</sup>*new

/8 (64, 1; *<sup>m</sup>*, *<sup>n</sup>*) *<sup>S</sup>*new

. .

. .

*θ*/8(*m* + 1, *n*) − *θ*/8(*m*, *n*)

master, slave 8-times interpolated

block 8-times interpolated

1024

� + �

64 ∑ *q*=1

> � + �

the SP as shown in Fig.6(d). That is, in this particular case, we shift the pixels as

/8 (1, 2; *<sup>m</sup>*, *<sup>n</sup>*) ... *<sup>S</sup>*new

/8 (2, 2; *<sup>m</sup>*, *<sup>n</sup>*) ... *<sup>S</sup>*new

/8 (64, 2; *<sup>m</sup>*, *<sup>n</sup>*) ... *<sup>S</sup>*new

. ... .

.

16 ∑ *p*=1

1024-look mean-filtered

interferogram

Using the Number of Singular Points for the Evaluation

original

8 × 2 pixel block

8-times interpolated

8-times interpolated

Table 1. Map status and notation

� � �

�

⎛

*S*new

*S*new

*S*new

⎜⎜⎜⎜⎜⎜⎜⎝

where

Fig. 7. The process of moving the slave: (a)Move **S**/8(*m*, *n*) by 1/8 pixel as *S*new /8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* − 1, *q* − 1; *m*, *n*) in order to erase the SP made by the 4 blocks, (b)replace back *S*new /8 (*p*, *q*; *m*, *n*) and do the same process to **S**/8(*m*, *n* + 1), (c)move *S*new /8 (*p*, *<sup>q</sup>*; *<sup>m</sup>*, *<sup>n</sup>*) by 1/8 pixel to a different direction, and (d)move *<sup>S</sup>*new /8 (*p*, *q*; *m*, *n*) by 2/8 pixels.

coordinate-system" maps, and the original ones as "1-pixel coordinate-system" maps. Table 1 lists the definitions used here, in which *I*/8(*m*, *n*) denotes the pixel value of interferogram in the 1/8-pixel coordinate system, and *I*(*m*, *n*) denotes the value in the 1-pixel coordinate system simply. Coordinate (*m*, *n*) stands for global position in the (16-look) mean-filtered interferogram, while (*p*, *q*) represents the local position in the 1/8-pixel coordinate system.

To get *I*/8(*m*, *n*), on the other hand, we need (8 × 8) × (2 × 8) = 1024 subpixels. Hence we regard these 1024 pixels as single blocks, **M**/8(*m*, *n*) and **S**/8(*m*, *n*), respectively.


### Table 1. Map status and notation

We first make an 1/8-pixel coordinate-system interferogram locally. The pixel value *I*/8(*m*, *n*), which corresponds to a pixel of a 16-look mean-filtered interferogram *I*(*m*, *n*), is calculated as

$$M\_{/8}(m,n) = \frac{1}{1024} \sum\_{q=1}^{64} \sum\_{p=1}^{16} M\_{/8}(p,q;m,n) \mathcal{S}\_{/8}^\*(p,q;m,n) \tag{9}$$

where *M*/8(*p*, *q*; *m*, *n*) represents the *p*-th top and *q*-th left pixel in the block **M**/8(*m*, *n*), while *S*/8(*p*, *q*; *m*, *n*) represents the *p*-th and *q*-th pixel in **S**/8(*m*, *n*) in the same manner. For example, if there is a SP at *I*/8(*m*, *n*), *I*/8(*m* + 1, *n*), *I*/8(*m*, *n* + 1), *I*/8(*m* + 1, *n* + 1) in the interferogram, as shown in Fig.6(c), we find non-zero rotation as

$$\begin{aligned} \left| \left( \theta\_{/8}(m+1,n) - \theta\_{/8}(m,n) \right) + \left( \theta\_{/8}(m,n) - \theta\_{/8}(m,n+1) \right) + \\\\ \left( \theta\_{/8}(m+1,n+1) - \theta\_{/8}(m+1,n) \right) + \left( \theta\_{/8}(m+1,n+1) - \theta\_{/8}(m,n+1) \right) \right| &\geq 2\pi \end{aligned} \tag{10}$$

where

8 Will-be-set-by-IN-TECH

16

64 16

64

master

master

slave

*new new*

/8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* − 1, *q* − 1; *m*, *n*) in order to erase the SP made by the 4 blocks,

/8 (*p*, *q*; *m*, *n*) and do the same process to **S**/8(*m*, *n* + 1), (c)move

coordinate-system" maps, and the original ones as "1-pixel coordinate-system" maps. Table 1 lists the definitions used here, in which *I*/8(*m*, *n*) denotes the pixel value of interferogram in the 1/8-pixel coordinate system, and *I*(*m*, *n*) denotes the value in the 1-pixel coordinate system simply. Coordinate (*m*, *n*) stands for global position in the (16-look) mean-filtered interferogram, while (*p*, *q*) represents the local position in the 1/8-pixel coordinate system.

To get *I*/8(*m*, *n*), on the other hand, we need (8 × 8) × (2 × 8) = 1024 subpixels. Hence we

regard these 1024 pixels as single blocks, **M**/8(*m*, *n*) and **S**/8(*m*, *n*), respectively.

slave

*new new*

(c)

Fig. 7. The process of moving the slave: (a)Move **S**/8(*m*, *n*) by 1/8 pixel as

/8 (*p*, *<sup>q</sup>*; *<sup>m</sup>*, *<sup>n</sup>*) by 1/8 pixel to a different direction, and (d)move *<sup>S</sup>*new

*S/8(m,n)*

*S/8(m, n+1)*

*S/8(m+1 ,n+1)*

*S/8(m+1 ,n)*

(a)

*S/8(m, n+1)*

*S/8(m+1 ,n+1)*

*S/8(m,n)*

*S/8(m+1 ,n)*

16

64 16

64

16

64 16

64

*S*new

*S*new

pixels.

(b)replace back *S*new

(b)

*S/8(m,n)*

*S/8(m, n+1)*

*S/8(m+1 ,n+1)*

*S/8(m+1 ,n)*

*S/8(m,n)*

*S/8(m, n+1)*

*S/8(m+1 ,n+1)*

*S/8(m+1 ,n)*

master

/8 (*p*, *q*; *m*, *n*) by 2/8

master

slave

slave

16

64 16

64

(d)

$$\theta\_{/8}(m,n) \equiv \arg(I\_{/8}(m,n)).\tag{11}$$

Simultaneously, in this square *I*/8(*m*, *n*)—*I*/8(*m* + 1, *n* + 1), there is local distortion in the master and / or the slave. Then we therefore move one or some of the blocks among the four **S**/8(*m*, *n*)—**S**/8(*m* + 1, *n* + 1) blocks to modify the interferogram. For example, we move **S**/8(*m*, *n*) locally in such a manner that *S*new /8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* + 1, *q* + 1; *m*, *n*) to try to erase the SP as shown in Fig.6(d). That is, in this particular case, we shift the pixels as

$$\begin{pmatrix} S\_{/8}^{\text{new}}(1,1;m,n) & S\_{/8}^{\text{new}}(1,2;m,n) & \dots & S\_{/8}^{\text{new}}(1,16;m,n) \\ S\_{/8}^{\text{new}}(2,1;m,n) & S\_{/8}^{\text{new}}(2,2;m,n) & \dots & S\_{/8}^{\text{new}}(2,16;m,n) \\ \vdots & \vdots & \ddots & \vdots \\ S\_{/8}^{\text{new}}(64,1;m,n) & S\_{/8}^{\text{new}}(64,2;m,n) & \dots & S\_{/8}^{\text{new}}(64,16;m,n) \end{pmatrix}\_{\text{\textquotedblleft}}$$

(a) (b)

10

20

30

10

<sup>105</sup> Local, Fine Co-Registration of SAR Interferometry

10

Using the Number of Singular Points for the Evaluation

20

30

10

20

30

10

20

30

10

20

30

10

20

30

20 60 100 140

20 60 100 140

20 60 100 140

20 60 100 140

20 60 100 140

20

30

20 60 100 140

(c) (d)

10

20

30

(e) (f)

10

20

30

(g) (h)

10

20

30

20 60 100 140

20 60 100 140

20 60 100 140

20 60 100 140

(i) (j)

Fig. 8. Interferogram and its SP plot for the black-square area in Fig.3(a): (a)Interferogram before the local co-registration process and (b)its SP plot (1,014 SPs), (c)result of the first iteration with 1-block shifts and (d)its SP plot (396 SPs), (e)result of the second iteration with 1-block shifts and (f)its SP plot (324 SPs), (g)result of 4-block shifts in addition and (h)its SP

plot (184 SPs), and (i)result of 9-block shifts in addition and (j)its SP plot (171 SPs).

$$\underbrace{\longleftrightarrow\limits\_{\begin{pmatrix}\mathcal{S}\_{/8}(1,1;m,n) & \mathcal{S}\_{/8}(1,1;m,n) & \dots & \mathcal{S}\_{/8}(1,16;m,n) \\ \mathcal{S}\_{/8}(2,1;m,n) & \mathcal{S}\_{/8}(1,1;m,n) & \dots & \mathcal{S}\_{/8}(1,15;m,n) \\ \vdots & \vdots & \ddots & \vdots \\ \mathcal{S}\_{/8}(64,1;m,n) & \mathcal{S}\_{/8}(63,1;m,n) & \dots & \mathcal{S}\_{/8}(63,15;m,n) \end{pmatrix}}}\_{\mathcal{S}\_{/8}(63,15;m,n)}\tag{12}$$

There are nesting stages in our method. First, we move the slave by 1/8 pixel and replace **S**/8(*m*, *n*) as *S*new /8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* − 1, *q* − 1; *m*, *n*) as shown in Fig.7(a). Then we check whether the SP disappears with this operation or not. If it does not, we move **S**/8(*m*, *n* + 1), **S**/8(*m* + 1, *n*), and **S**/8(*m* + 1, *n* + 1) in the slave in turn, in the same direction (Fig.7(b)). If it is impossible to erase the SP with the above up-leftward movements, we employ other seven directions (Fig.7(c)). Then for the remaining SPs, we try 2/8 shifts in the same way (Fig.7(d)). If the SP cannot be removed with up to 8/8(=1) shifts, we abandon the elimination of the SP there, and try to erase the next one in the interferogram.

We apply the above process to all of the SPs in the interferogram iteratively. If we find that there is no erasable SP any more, we apply a similar shifting process for 4 (=2 × 2) big blocks. For example, we shift **S**/8(*m*, *n*), **S**/8(*m*, *n* + 1), **S**/8(*m* + 1, *n*), and **S**/8(*m* + 1, *n* + 1) simultaneously as a single large block.

$$\begin{pmatrix} S\_{/8}^{\mathrm{new}}(1,1;m,n) & S\_{/8}^{\mathrm{new}}(1,2;m,n) & \dots & S\_{/8}^{\mathrm{new}}(1,16;m,n+1) \\ S\_{/8}^{\mathrm{new}}(2,1;m,n) & S\_{/8}^{\mathrm{new}}(2,2;m,n) & \dots & S\_{/8}^{\mathrm{new}}(2,16;m,n+1) \\ \vdots & \vdots & \ddots & \vdots \\ S\_{/8}^{\mathrm{new}}(64,1;m+1,n) & S\_{/8}^{\mathrm{new}}(64,2;m+1,n) & \dots & S\_{/8}^{\mathrm{new}}(64,16;m+1,n+1) \end{pmatrix}$$

$$\longleftrightarrow \begin{pmatrix} S\_{/8}(1,1;m,n) & S\_{/8}(1,1;m,n) & \dots & S\_{/8}(1,16;m,n+1) \\ S\_{/8}(2,1;m,n) & S\_{/8}(1,1;m,n) & \dots & S\_{/8}(1,15;m,n+1) \\ \vdots & \vdots & \ddots & \vdots \\ S\_{/8}(64,1;m+1,n) & S\_{/8}(63,1;m+1,n) & \dots & S\_{/8}(63,15;m+1,n+1) \end{pmatrix} \tag{13}$$

We can also apply a 9 (=3 × 3) bigger block movement afterward, if needed.

### **4. Experimental results**

Figure 8 presents the changes of the phase map and corresponding SP distributions when we apply the SPEC method. The shown area is the black-squared part in Fig.3(a). As shown in Figs.8(a) and (b), there were 1,014 SPs in the original interferogram. The first iteration in our proposed method erased more than 60 percent of them, resulting in 396 SPs (Figs.8(c) and (d)). In the second iteration, 324 points left (Figs.8(e) and (f)). For the present data, with 1-block movement, no SP was erased anymore. With the additional 4-block move, our proposed method decreased the SP number to 184 (Figs.8(g) and (h)). With the 9-block move, our method decreased the SP number to 171 (Figs.8(i) and (j)), where our method finally erased about 83% of the SPs in the original interferogram. Figures 9(a) and 9(b) show the resulting interferogram and its SP plot for the data in Fig.3(a). The number of the SPs decreased from 11,518 to 1,865. The decreasing ratio was about 83% again for the whole interferogram.

Figure 10 compares (a) the true height map and the results of the unwrapping by the iterative least-square (LS) techniqueSuksmono & Hirose (2006) (b) with and (c) without the SPEC 10 Will-be-set-by-IN-TECH

There are nesting stages in our method. First, we move the slave by 1/8 pixel and replace

whether the SP disappears with this operation or not. If it does not, we move **S**/8(*m*, *n* + 1), **S**/8(*m* + 1, *n*), and **S**/8(*m* + 1, *n* + 1) in the slave in turn, in the same direction (Fig.7(b)). If it is impossible to erase the SP with the above up-leftward movements, we employ other seven directions (Fig.7(c)). Then for the remaining SPs, we try 2/8 shifts in the same way (Fig.7(d)). If the SP cannot be removed with up to 8/8(=1) shifts, we abandon the elimination

We apply the above process to all of the SPs in the interferogram iteratively. If we find that there is no erasable SP any more, we apply a similar shifting process for 4 (=2 × 2) big blocks. For example, we shift **S**/8(*m*, *n*), **S**/8(*m*, *n* + 1), **S**/8(*m* + 1, *n*), and **S**/8(*m* + 1, *n* + 1)

. ... .

.

Figure 8 presents the changes of the phase map and corresponding SP distributions when we apply the SPEC method. The shown area is the black-squared part in Fig.3(a). As shown in Figs.8(a) and (b), there were 1,014 SPs in the original interferogram. The first iteration in our proposed method erased more than 60 percent of them, resulting in 396 SPs (Figs.8(c) and (d)). In the second iteration, 324 points left (Figs.8(e) and (f)). For the present data, with 1-block movement, no SP was erased anymore. With the additional 4-block move, our proposed method decreased the SP number to 184 (Figs.8(g) and (h)). With the 9-block move, our method decreased the SP number to 171 (Figs.8(i) and (j)), where our method finally erased about 83% of the SPs in the original interferogram. Figures 9(a) and 9(b) show the resulting interferogram and its SP plot for the data in Fig.3(a). The number of the SPs decreased from 11,518 to 1,865. The decreasing ratio was about 83% again for the whole interferogram.

Figure 10 compares (a) the true height map and the results of the unwrapping by the iterative least-square (LS) techniqueSuksmono & Hirose (2006) (b) with and (c) without the SPEC

*S*/8(1, 1; *m*, *n*) *S*/8(1, 1; *m*, *n*) ... *S*/8(1, 16; *m*, *n* + 1) *S*/8(2, 1; *m*, *n*) *S*/8(1, 1; *m*, *n*) ... *S*/8(1, 15; *m*, *n* + 1)

*S*/8(64, 1; *m* + 1, *n*) *S*/8(63, 1; *m* + 1, *n*) ... *S*/8(63, 15; *m* + 1, *n* + 1)

/8 (1, 2; *<sup>m</sup>*, *<sup>n</sup>*) ... *<sup>S</sup>*new

/8 (2, 2; *<sup>m</sup>*, *<sup>n</sup>*) ... *<sup>S</sup>*new

/8 (64, 2; *<sup>m</sup>* <sup>+</sup> 1, *<sup>n</sup>*) ... *<sup>S</sup>*new

. .

We can also apply a 9 (=3 × 3) bigger block movement afterward, if needed.

. .

. .

*S*/8(1, 1; *m*, *n*) *S*/8(1, 1; *m*, *n*) ... *S*/8(1, 16; *m*, *n*) *S*/8(2, 1; *m*, *n*) *S*/8(1, 1; *m*, *n*) ... *S*/8(1, 15; *m*, *n*)

*S*/8(64, 1; *m*, *n*) *S*/8(63, 1; *m*, *n*) ... *S*/8(63, 15; *m*, *n*)

/8 (1, 16; *m*, *n* + 1)

/8 (2, 16; *m*, *n* + 1)

. .

/8 (64, 16; *m* + 1, *n* + 1)

. ... .

. ... .

. .

⎞

⎟⎟⎟⎟⎠

⎞

⎟⎟⎟⎠

(13)

. . ⎞

⎟⎟⎟⎠

(12)

.

/8 (*p*, *q*; *m*, *n*) ← *S*/8(*p* − 1, *q* − 1; *m*, *n*) as shown in Fig.7(a). Then we check

←−

**S**/8(*m*, *n*) as *S*new

⎛

*S*new

*S*new

*S*new

. .

←−

**4. Experimental results**

⎜⎜⎜⎜⎝

⎛

⎜⎜⎜⎝

of the SP there, and try to erase the next one in the interferogram.

.

simultaneously as a single large block.

/8 (1, 1; *<sup>m</sup>*, *<sup>n</sup>*) *<sup>S</sup>*new

/8 (2, 1; *<sup>m</sup>*, *<sup>n</sup>*) *<sup>S</sup>*new

/8 (64, 1; *<sup>m</sup>* <sup>+</sup> 1, *<sup>n</sup>*) *<sup>S</sup>*new

⎛

⎜⎜⎜⎝

. .

. .

Fig. 8. Interferogram and its SP plot for the black-square area in Fig.3(a): (a)Interferogram before the local co-registration process and (b)its SP plot (1,014 SPs), (c)result of the first iteration with 1-block shifts and (d)its SP plot (396 SPs), (e)result of the second iteration with 1-block shifts and (f)its SP plot (324 SPs), (g)result of 4-block shifts in addition and (h)its SP plot (184 SPs), and (i)result of 9-block shifts in addition and (j)its SP plot (171 SPs).

50

Using the Number of Singular Points for the Evaluation

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and (c)without the SPEC method (Mt. Fuji).

50 100 150 200 250 300 Position *n*

<sup>107</sup> Local, Fine Co-Registration of SAR Interferometry

50 100 150 200 250 300 Position *n*

50 100 150 200 250 300 Position *n*

(c) Fig. 10. (a)True height map and DEMs obtained by the iterative least square technique(b)with

(b)

(a)

2000

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(a) (b) Fig. 9. (a)Interferogram made by the proposed SPEC method for the data shown in Fig.3(a) and (b)its SP plot (# SPs = 1,865).

method. We find improvement in some regions in the SPEC result in (b). For example, the dotted-square region in Fig.10(b) (zoomed in Fig. 11 ) shows more accurate ridges than those in Fig.10(c). It is obvious that the valleys and edges in Fig.11(b) are more distinct than those in Fig.11(c). We compared the mean signal-to-noise ratio (MSNR) (≡ squared height range / mean squared error) and the peak signal-to-noise ratio (PSNR) (≡ squared height range / peak squared error) based on the true data. The DEM with the SPEC method resulted in *MSNR* = 29.5[dB] and *PSNR* = 14.5[dB]. On the other hand, the DEM without our method resulted in *MSNR* = 27.2[dB] and *PSNR* = 14.3[dB]. The SPEC method improved the quality of the DEM both in average and at the peak.

We intend that our SPEC method compensates the local phase distortions in the interferogram. As this ability is similar to filtering (i.e., phase estimation), we calculated whether the SNR of the filtered interferogram changes if we co-register the interferogram with our proposed method. We used the iterative LS technique for unwrapping and the complex-valued Markov random field model (CMRF) filter Yamaki & Hirose (2009) for this evaluation. We compared the results for filtered interferograms of Mt. Fuji with those of non-filtered ones, which are co-registered with and without our SPEC method.


Table 2. MSNR and PSNR of Mt. Fuji's DEMs unwrapped by the iterative LS

Table 2 shows the results of this experiment. The CMRF filter increased the SNRs of the DEMs of Mt. Fuji. Table 2 shows that the use of the SPEC method could not improve the MSNR of Mt. Fuji. The reason of this result is that the shape of the mountains and the phase ambiguity led to this result. Mt. Fuji has an ordinary single volcanic cone shape with clear fringes. Basically, phase estimation works good when the interferogram has clear fringes. As our SPEC method is an additional step of co-registration, it decreases the number of SPs and make fringes clearer 12 Will-be-set-by-IN-TECH

Position *m*

50 100 150 200 250 300 Position *n*

−2π

2π

*0*

π

*0*

−π

(b) Fig. 9. (a)Interferogram made by the proposed SPEC method for the data shown in Fig.3(a)

method. We find improvement in some regions in the SPEC result in (b). For example, the dotted-square region in Fig.10(b) (zoomed in Fig. 11 ) shows more accurate ridges than those in Fig.10(c). It is obvious that the valleys and edges in Fig.11(b) are more distinct than those in Fig.11(c). We compared the mean signal-to-noise ratio (MSNR) (≡ squared height range / mean squared error) and the peak signal-to-noise ratio (PSNR) (≡ squared height range / peak squared error) based on the true data. The DEM with the SPEC method resulted in *MSNR* = 29.5[dB] and *PSNR* = 14.5[dB]. On the other hand, the DEM without our method resulted in *MSNR* = 27.2[dB] and *PSNR* = 14.3[dB]. The SPEC method improved the quality

We intend that our SPEC method compensates the local phase distortions in the interferogram. As this ability is similar to filtering (i.e., phase estimation), we calculated whether the SNR of the filtered interferogram changes if we co-register the interferogram with our proposed method. We used the iterative LS technique for unwrapping and the complex-valued Markov random field model (CMRF) filter Yamaki & Hirose (2009) for this evaluation. We compared the results for filtered interferograms of Mt. Fuji with those of non-filtered ones, which are

Without filter MSNR [dB] 27.2 29.5

Table 2 shows the results of this experiment. The CMRF filter increased the SNRs of the DEMs of Mt. Fuji. Table 2 shows that the use of the SPEC method could not improve the MSNR of Mt. Fuji. The reason of this result is that the shape of the mountains and the phase ambiguity led to this result. Mt. Fuji has an ordinary single volcanic cone shape with clear fringes. Basically, phase estimation works good when the interferogram has clear fringes. As our SPEC method is an additional step of co-registration, it decreases the number of SPs and make fringes clearer

With the CMRF filter MSNR [dB] 35.8 34.9

Table 2. MSNR and PSNR of Mt. Fuji's DEMs unwrapped by the iterative LS

Co-registration Without SPEC method With SPEC method

PSNR [dB] 14.3 14.5

PSNR [dB] 19.2 19.7

50 100 150 200 250 300 Position *n*

(a)

of the DEM both in average and at the peak.

co-registered with and without our SPEC method.

❵❵❵❵❵❵❵❵❵❵

❵

Filtering

and (b)its SP plot (# SPs = 1,865).

Position *m*

(c) Fig. 10. (a)True height map and DEMs obtained by the iterative least square technique(b)with and (c)without the SPEC method (Mt. Fuji).

before the CMRF filter works. That is why the CMRF filter could estimate the fringes of the

<sup>109</sup> Local, Fine Co-Registration of SAR Interferometry

We proposed a new method of co-registration, namely, the SPEC method. This method uses the number of SPs in the temporary interferogram as the evaluation criterion to co-register the master and slave maps locally and nonlinearly. By applying our method to real data, we found that the SPEC method successfully improves the quality of the DEM in many cases.At the same time, we found that the SPEC method make ambiguous fringes clearer in its appearance. Our present method uses only the number of singular points as the evaluation criterion. In the future, we have the possibility to use other information, in addition to the SP number, to

The authors would like to thank Dr. M. Shimada of EORC/JAXA, Japan, for supplying the

Boerner, W. M. (2003). "Recent advances in extra-wide-band polarimetry, interferometry

Costantini, M. (1998). "A Novel Phase Unwrapping Method Based on Network

Ferraiuolo, G. & Poggi, G. (2004), "A Bayesian Filtering Technique for SAR Interferometric

Fornaro, G.; Franceschetti, G., & Lanari, G. (1996) "Interferometric SAR phase unwrapping

Gabriel, A. K.; Goldstein, R. M. & Zebker, H. A. (1989). "Mapping small elevation changes

Ghiglia, D. C. & Pritt, M. D. (1998). "Two-Dimensional Phase Unwrapping : Theory,"

Goldstein, R. and Werner, C. (1998). "Radar interferogram filtering for geophysical

Hajnsek, I.; Jagdhuber, T.; Schon, H. & Papathanassiou, K. P. (2009). "Potential of Estimating

*Algorithms, and Software. John Wiley and Sons, Inc.*, 1998.

*and Remote Sensing*, Vol.47, No.2, pp. 442-454, February 2009.

and polarimetric interferometry in synthetic aperture remote sensing and its applications," *IEE Proceedings Radar, Sonar and Navigation,* Vol.150, No.3, pp.113-124,

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over large areas: Differential interferometry," Journal of Geophysical Research, vol.

applications,"*Geophysical Research Letters*, vol. 25, no. 21, pp. 4035-4038, November

Soil Moisture Under Vegetation Cover by PolSAR," *IEEE Transactions on Geoscience*

interferogram more precisely.

Using the Number of Singular Points for the Evaluation

improve the performance further.

InSAR data and the height data for evaluation.

**6. Acknowledgment**

June 2003.

813-821, May 1998.

34, no. 3, pp. 720-727, May 1996.

94, pp. 9183-9191, July 1989.

October 2004.

1998.

**7. References**

**5. Conclusion**

(c) Fig. 11. Dotted square part of Fig.10. (a)True height map and DEMs obtained (b)with and (c)without the SPEC method.

before the CMRF filter works. That is why the CMRF filter could estimate the fringes of the interferogram more precisely.

### **5. Conclusion**

14 Will-be-set-by-IN-TECH

Position *n*

(a)

Position *n*

(b)

Position *n*

(c) Fig. 11. Dotted square part of Fig.10. (a)True height map and DEMs obtained (b)with and

50 100

50 100

50 100

2000

2500

1500

1000

500

0

2000

2500

1500

1000

500

0

2000

2500

1500

1000

500

0

50

Position *m*

100

50

Position *m*

100

50

Position *m*

100

(c)without the SPEC method.

We proposed a new method of co-registration, namely, the SPEC method. This method uses the number of SPs in the temporary interferogram as the evaluation criterion to co-register the master and slave maps locally and nonlinearly. By applying our method to real data, we found that the SPEC method successfully improves the quality of the DEM in many cases.At the same time, we found that the SPEC method make ambiguous fringes clearer in its appearance. Our present method uses only the number of singular points as the evaluation criterion. In the future, we have the possibility to use other information, in addition to the SP number, to improve the performance further.

### **6. Acknowledgment**

The authors would like to thank Dr. M. Shimada of EORC/JAXA, Japan, for supplying the InSAR data and the height data for evaluation.

### **7. References**


**6** 

Hai Li and Renbiao Wu

*P.R. China* 

*Tianjin Key Lab for Advanced Signal Processing, Civil Aviation University of China, Tianjin,* 

**Robust Interferometric Phase Estimation** 

Synthetic aperture radar interferometry (InSAR) is an important remote sensing technique to retrieve the terrain digital elevation model (DEM)[1][2]. Image coregistration, InSAR interferometric phase estimation (or noise filtering) and interferometric phase unwrapping[3][4][5][6] are three key processing procedures of InSAR. It is well known that the performance of interferometric phase estimation suffers seriously from poor image

Image coregistration is an important preprocessing operation that aligns the pixels of one image to the corresponding pixels of another image. A review of recent as well as classic image registration methods can be found in Ref.[7]. Mutual information used for the registration of remote sensing imagery are presented in the literature[8]. In literature[9], the feature-based registration methods are presented. A new direct Fourier-transform-based algorithm for subpixel registration is proposed in Ref.[10]. In Ref.[11], a geometrical approach for image registration of SAR images is proposed, and the algorithm has been tested on several real data. A image registration method based on isolated point scatterers is

Almost all the conventional InSAR interferometric phase estimation methods are based on interferogram filtering[13][14][15][16][17][18], such as pivoting mean filtering[13], pivoting median filtering[14], adaptive phase noise filtering[15], and adaptive contoured window filtering[18]. However, when the quality of an interferogram is very poor due to a large coregistration error, it is very difficult for these methods to retrieve the true terrain interferometric phases. In fact, the interferometric phases are random in nature with their variances being inversely proportional to the correlation coefficients between the corresponding pixel pairs of the two coregistered SAR images[2]. Therefore, the terrain

In this chapter, the interferometric phase estimation method based on subspace projection and its modified version were proposed. Theoretical analysis and computer simulation results show that the methods can provide accurate estimation of the terrain interferometric phase (interferogram) even if the coregistration error reaches one pixel. The remainder of this chapter is organized as follows. Section 2 presents the signal model of a single pixel pair

**1. Introduction** 

coregistration.

proposed in Ref.[12].

interferometric phases should be estimated statistically.

**in InSAR via Joint Subspace Projection** 

