**4. Verification results for real-life SAR images**

accuracy and the influence of estimation variance *θ<sup>μ</sup>*

accuracy has to be characterized not by *<sup>ε</sup>* <sup>2</sup> but by *ε*/*σ<sup>μ</sup>*

has the tendency to make worse if *σ<sup>μ</sup>*

318 Computational and Numerical Simulations

accurately estimate speckle variance *σ<sup>μ</sup>*

^ *μ*

results for single-look images are collected in Table 2.

2 and the true value *σ<sup>μ</sup>*

due to pre-segmentation), this method provides smaller estimates *σ*

As it can be also seen from analysis of data in Table 2, the estimates *σ*

variance to the *ε* <sup>2</sup>

**Table 2.** The values of σ

^ μ <sup>2</sup> -σμ

the obtained estimate *σ*

2

. Thus, below we present only the errors determined as the difference between

more observation is that the values of *ε* <sup>2</sup> for multi-look test images have become smaller than for single-look test images. This does not mean that accuracy has improved since, in fact,

Consider now the case of spatially correlated noise. We have carried out preliminary simula‐ tions and established that estimation bias contributes considerably more than estimation

**Method Method 1 Method 2 Method 3 Block size 5x5 7x7 5x5 7x7 5x5 7x7** Image Fr01 -0.0097 0.0178 0.0056 0.0041 -0.0348 -0.0138 Image Fr02 -0.0107 0.0148 -0.0070 0.0282 -0.0207 -0.0206 Image Fr03 -0.0089 0.0151 -0.0059 0.0305 -0.0194 -0.0116 Image Fr04 -0.0142 0.0103 0.0019 0.0355 -0.0408 -0.0294

2 for the test single-look images corrupted by spatially correlated noise (σμ

An interesting observation that follows from data analysis in Table 2 is that the differences are mostly negative, at least, for 5x5 block size, i.e. speckle variance is underestimated. This can be explained as follows. One factor that influences blind estimation is distribution mode position. Normal local estimates in blocks that form this mode are mostly smaller than *σ<sup>μ</sup>*

(Lukin et al., 2011b). Because of this, speckle variance estimates tend to smaller values for **Method 1**, cluster centers tend to smaller values for **Method 2** and **Method 3** as well. Another factor is the method robustness with respect to abnormal local estimates which are, recall, larger than normal estimates. These abnormal local estimates "draw" the final estimates to another side, i.e. "force" them to be larger. Thus, these two factors partly compensate each other. Since **Method 3** is more robust with respect to outliers (a large part of them is rejected

than the corresponding estimates for 5x5 blocks. This is because mode position for normal local estimates shifts to right (to larger values) if the block size increases. This effects have been illustrated for spatially correlated speckle (Lukin et al., 2011b) and for spatially correlated additive noise (Abramov et al., 2008). Then, the final estimates for all BENCs also increase.

can be ignored in further studies. One

<sup>2</sup> . In fact, accuracy characterized by *ε*/*σ<sup>μ</sup>*

2 diminishes. This means that it is more difficult to

2 for multi-look SAR images than for single-look ones.

2 for single (only one) realization. The simulation

^ *μ* 2 .

^ *μ* 2=0.273)

2 for 7x7 blocks are larger

2

2

First, we will verify our BENCs for the single-look real-life TerraSAR-X images presented in Figures 5 and 7. The obtained data will be considered in subsection 4.1. Besides, in subsection 4.2, we will verify our BENCs for multi-look SAR images of urban area in Canada (Toronto) (these images are presented later). All of them are acquired for HH polarization. As it is stated in file description, approximate number of looks is about 6. Thus, the expected *σμ* <sup>2</sup> <sup>≈</sup>0.273 / <sup>6</sup>≈0.045. Similarly, assuming *σ<sup>μ</sup>* <sup>2</sup> =0.045 for multi-look data, we can get the limits 0.036…0.054 for blind estimates that can be considered appropriate in practice. Let us keep these limits in mind in further analysis.

### **4.1. Verification results for single-look SAR images**

Let us start from data obtained for **Method 1**. The estimates for block sizes 5x5, 7x7 and 9x9 pixels are collected in Table 4. We decided to analyse 9x9 blocks (not exploited in simulations) to understand practical tendencies and to be sure in our recommendations. Analysis shows that the estimates for 9x9 blocks are larger than for 7x7 and 5x5 blocks. Moreover, for the image in Fig. 5(a) the blind estimate is outside the desired limits. This happens because this image has complex structure and a large percentage of local estimates are abnormal. Although **Method 1** is robust with respect to outliers, its robustness is not enough to keep the blind estimate within the required limits.


Concerning other blind estimates, they all are within the required limits. For three of four reallife images, 7x7 block size is the best choice from the viewpoint of estimation accuracy.

**Table 4.** Blind estimates of speckle variance for single-look real-life SAR images obtained by Method 1

Let us consider the results for two other BENC methods, both based on scatter-plots. Here we consider only the case of 7x7 blocks according to recommendations given in the previous Section. The estimates obtained by the **Method 2** for single-look images (Figs. 5 and 7) are, within the required limits (see data in Table 5) for three of four processed images. The only exception is again the image in Fig. 5(a), due to complexity of its structure. In general, the estimates for the **Method 2** are larger and less accurate than for the **Method 1 (**see data in Table 4) for 7x7 blocks. We have the following explanation for that. It is quite difficult to provide unbiased estimates of cluster centers especially for those clusters that contain a relatively small number of points. Then, biasedness of cluster center estimates leads to final overestimation of speckle variance for **Method 2**.

Table 5 also contains blind estimates obtained by **Method 3**. All the estimates are within the required limits and they are, in general, more accurate than for other two methods. These conclusions also follow from analysis carried out by us for twenty 512x512 fragments of reallife SAR images (the data for 12 images are presented in Lukin et al., 2011b).

The obtained blind estimates for **Method 1** (three block sizes) are collected in Table 6. As it is seen, for 5x5 blocks they are mostly smaller than desired (the lower margin is 0.036), for 7x7 blocks all estimates are within the required limits (from 0.036 to 0.054), and two out of four estimates are larger than desired 0.054) for 9x9 blocks. Thus, 7x7 blocks are again the proper choice for **Method 1**. We would like to stress also that the estimate for the most complex image in Fig. 10(d) is always the largest for any given block size. To our experience, this is due to the

The obtained blind estimates for **Method 1** (three block sizes) are collected in Table 6. As it is seen, for 5x5 blocks they are mostly smaller than desired (the lower margin is 0.036), for 7x7 blocks all estimates are within the required limits (from 0.036 to 0.054), and two out of four estimates are larger than desired 0.054) for 9x9 blocks. Thus, 7x7 blocks are again the proper choice for **Method 1**. We would like to stress also that the estimate for the most complex image in Fig. 10(d) is always the largest for any given block size. To our experience, this is due to the influence of image content (large percentage of abnormal local estimates).

The real-life six-look SAR images used in verification tests are given in Fig. 10. From visual inspection, the image in Fig. 10(d) seems to have more complex structures whilst other three images have quite large quasi-homogeneous regions. Let us see how this will influence

0 1 2 3 4 5 6 7

10(a) 0.033 0.042 0.043 10(b) 0.034 0.048 0.055 10(c) 0.033 0.045 0.051 10(d) 0.038 0.053 0.061

**Block size 5x5 7x7 9x9**

x 104

**Used method Method 2, 7x7 blocks Method 3, 7x7 blocks**

http://dx.doi.org/10.5772/57040

321

Used method **Method 2**, 7x7 blocks **Method 3**, 7x7 blocks

5(a) 0.353 0.296 5(b) 0.289 0.259 7(a) 0.315 0.255 7(b) 0.315 0.266

5(a) 0.353 0.296 5(b) 0.289 0.259 7(a) 0.315 0.255 7(b) 0.315 0.266 Table 5. Blind estimates of speckle variance for single-look real-life SAR images obtained by

An example of such scatter-plot obtained as (6) for image with clipping effects is given in Fig. 9. Straight line shows the true position of the line to be fitted. As it is seen, there are three clusters (that correspond to large means) positions which are erroneous (vertical coordinates are considerably smaller than they should be). Although line fitting method is robust, the presence of a large percentage of such clusters can lead to essential errors in

Methods for Blind Estimation of Speckle Variance in SAR Images: Simulation Results and Verification for Real-Life Data

**Table 5.** Blind estimates of speckle variance for single-look real-life SAR images obtained by Method 2 and Method 3

influence of image content (large percentage of abnormal local estimates).

0

**4.2 Verification results for multi-look SAR images**

Fig. 9. Scatter-plot for image with clipping effects

0.5

1

1.5

2

2.5 x 104

**Table 6.** Blind estimates of speckle variance for six-look real-life SAR images obtained by Method 1

**Image presented in Figure**

blind estimates.

**Figure 9.** Scatter-plot for image with clipping effects

**Image presented in Figure**

blind estimation.

Image presented in Figure

**Method 2** and **Method 3** 

One more advantage of **Method 3** is that it is able to cope with image clipping effects. Note that clipping effects can arise due to limited range of image representation or incorrect scaling (Foi, 2009).

An example of such scatter-plot obtained as (6) for image with clipping effects is given in Fig. 9. Straight line shows the true position of the line to be fitted. As it is seen, there are three clusters (that correspond to large means) positions which are erroneous (vertical coordinates are considerably smaller than they should be). Although line fitting method is robust, the presence of a large percentage of such clusters can lead to essential errors in blind estimation.

### **4.2. Verification results for multi-look SAR images**

The real-life six-look SAR images used in verification tests are given in Fig. 10. From visual inspection, the image in Fig. 10(d) seems to have more complex structures whilst other three images have quite large quasi-homogeneous regions. Let us see how this will influence blind estimates.

Methods for Blind Estimation of Speckle Variance in SAR Images: Simulation Results and Verification for Real-Life Data http://dx.doi.org/10.5772/57040 321


**Table 5.** Blind estimates of speckle variance for single-look real-life SAR images obtained by Method 2 and Method 3 7(b) 0.315 0.266 Table 5. Blind estimates of speckle variance for single-look real-life SAR images obtained by

7(a) 0.315 0.255

**Figure 9.** Scatter-plot for image with clipping effects

Fig. 9. Scatter-plot for image with clipping effects

**4.2 Verification results for multi-look SAR images**

**Method 2** and **Method 3** 

Concerning other blind estimates, they all are within the required limits. For three of four reallife images, 7x7 block size is the best choice from the viewpoint of estimation accuracy.

> 5(a) 0.292 0.322 0.348 5(b) 0.250 0.265 0.274 7(a) 0.240 0.270 0.283 7(b) 0.241 0.269 0.277

Let us consider the results for two other BENC methods, both based on scatter-plots. Here we consider only the case of 7x7 blocks according to recommendations given in the previous Section. The estimates obtained by the **Method 2** for single-look images (Figs. 5 and 7) are, within the required limits (see data in Table 5) for three of four processed images. The only exception is again the image in Fig. 5(a), due to complexity of its structure. In general, the estimates for the **Method 2** are larger and less accurate than for the **Method 1 (**see data in Table 4) for 7x7 blocks. We have the following explanation for that. It is quite difficult to provide unbiased estimates of cluster centers especially for those clusters that contain a relatively small number of points. Then, biasedness of cluster center estimates leads to final overestimation of

Table 5 also contains blind estimates obtained by **Method 3**. All the estimates are within the required limits and they are, in general, more accurate than for other two methods. These conclusions also follow from analysis carried out by us for twenty 512x512 fragments of real-

One more advantage of **Method 3** is that it is able to cope with image clipping effects. Note that clipping effects can arise due to limited range of image representation or incorrect scaling

An example of such scatter-plot obtained as (6) for image with clipping effects is given in Fig. 9. Straight line shows the true position of the line to be fitted. As it is seen, there are three clusters (that correspond to large means) positions which are erroneous (vertical coordinates are considerably smaller than they should be). Although line fitting method is robust, the presence of a large percentage of such clusters can lead to essential errors in blind estimation.

The real-life six-look SAR images used in verification tests are given in Fig. 10. From visual inspection, the image in Fig. 10(d) seems to have more complex structures whilst other three images have quite large quasi-homogeneous regions. Let us see how this will influence blind

life SAR images (the data for 12 images are presented in Lukin et al., 2011b).

**4.2. Verification results for multi-look SAR images**

**Table 4.** Blind estimates of speckle variance for single-look real-life SAR images obtained by Method 1

**Block size 5x5 7x7 9x9**

**Image presented in Figure**

320 Computational and Numerical Simulations

speckle variance for **Method 2**.

(Foi, 2009).

estimates.

The obtained blind estimates for **Method 1** (three block sizes) are collected in Table 6. As it is seen, for 5x5 blocks they are mostly smaller than desired (the lower margin is 0.036), for 7x7 blocks all estimates are within the required limits (from 0.036 to 0.054), and two out of four estimates are larger than desired 0.054) for 9x9 blocks. Thus, 7x7 blocks are again the proper choice for **Method 1**. We would like to stress also that the estimate for the most complex image in Fig. 10(d) is always the largest for any given block size. To our experience, this is due to the influence of image content (large percentage of abnormal local estimates). The real-life six-look SAR images used in verification tests are given in Fig. 10. From visual inspection, the image in Fig. 10(d) seems to have more complex structures whilst other three images have quite large quasi-homogeneous regions. Let us see how this will influence blind estimates. The obtained blind estimates for **Method 1** (three block sizes) are collected in Table 6. As it is seen, for 5x5 blocks they are mostly smaller than desired (the lower margin is 0.036), for 7x7 blocks all estimates are within the required limits (from 0.036 to 0.054), and two out of four estimates are larger than desired 0.054) for 9x9 blocks. Thus, 7x7 blocks are again the proper choice for **Method 1**. We would like to stress also that the estimate for the most complex image in Fig. 10(d) is always the largest for any given block size. To our experience,


this is due to the influence of image content (large percentage of abnormal local estimates).

**Table 6.** Blind estimates of speckle variance for six-look real-life SAR images obtained by Method 1

**Figure 10.** Multi-look SAR elementary images (512x512 pixels) of urban region in Canada

Image presented

Finally, **Methods 2** and **3** have been verified for six-look images. The estimates are presented in Table 7 for 7x7 blocks. **Method 2** produces obvious overestimation (only one estimate is within the required interval and other ones exceed the upper limit). In turn, **Method 3** provides all four estimates accurate enough although underestimation is observed for all four processed images. Thus, **Method 3** operating in 7x7 blocks provides the best or nearly the best accuracy for all considered simulated and real-life images. in Figure 5x5 7x7 9x9 10(a) 0.033 0.042 0.043 10(b) 0.034 0.048 0.055 10(c) 0.033 0.045 0.051 10(d) 0.038 0.053 0.061 Table 6. Blind estimates of speckle variance for six-look real-life SAR images obtained by **Method 1** 

Block size

partly remove local estimates expected to be abnormal (due to block heterogeneity or to presence of clipping effects) is desirable. Such pre-processing might include image presegmentation which in our experiments has been performed by unsupervised variational classification through image multi-thresholding (Klaine et al., 2005). Its advantage is that preprocessing is quite fast. This allows obtaining blind estimates quite quickly since other

Methods for Blind Estimation of Speckle Variance in SAR Images: Simulation Results and Verification for Real-Life Data

**Used method Method 2, 7x7 blocks Method 3, 7x7 blocks**

http://dx.doi.org/10.5772/57040

323

operations (obtaining of local estimates and robust regression) are also very fast.

10(a) 0.051 0.041 10(b) 0.061 0.038 10(c) 0.089 0.036 10(d) 0.094 0.044

**Table 7.** Blind estimates of speckle variance for six-look real-life SAR images obtained by Method 2 and Method 3

Some aspects of SAR image simulation have been considered. In particular, it has been stressed that spatial correlation of speckle is to be taken into account. One algorithm to do this is

Three methods for blind estimation of noise statistical characteristics in SAR images have been first tested for simulated images. It has been shown that there are several factors influencing their performance. These factors are image content (complexity), the method used and its parameters. It is not always possible to provide blind estimates within desired limits especially for highly textural (complex structure) images. Then, these methods have been verified for real life TerraSAR-X images of limited size of 512x512 pixels. Preliminary tests have clearly demonstrated the presence of essential spatial correlation of speckle, especially for multi-look images. This is taken into account in setting parameters of BENC methods. The block size of

The BENC methods based on scatter-plots without image pre-processing produce, on the average, worse accuracy than the method based on mode determination for local estimates' distribution. If pre-processing is applied, BENC methods (as **Method 3**) are able to produce acceptable accuracy for most images. Estimation accuracy for single-look images is mostly acceptable. However, there are more problems with speckle variance estimation for multi-look images. Thus, in future, special attention should be paid to considering multi-look image case. In this sense, the methods based in obtaining noise-informative maps (Uss et al. 2011; Uss et al., 2012) seem to be attractive although they are not so fast as the methods considered above. This work has been partly supported by French-Ukrainian program Dnipro (PHC DNIPRO

**Image presented in Figure**

described.

**5. Conclusions and future work**

7x7 pixels is recommended for practical use.

2013, PROJET N° 28370QL).

The presented results clearly show that for estimation techniques based on scatter-plots and robust fitting it is often not enough to carry out robust fitting. Image pre-processing able to Finally, **Methods 2** and **3** have been verified for six-look images. The estimates are presented in Table 7 for 7x7 blocks. **Method 2** produces obvious overestimation (only one estimate is partly remove local estimates expected to be abnormal (due to block heterogeneity or to presence of clipping effects) is desirable. Such pre-processing might include image presegmentation which in our experiments has been performed by unsupervised variational classification through image multi-thresholding (Klaine et al., 2005). Its advantage is that preprocessing is quite fast. This allows obtaining blind estimates quite quickly since other operations (obtaining of local estimates and robust regression) are also very fast.


**Table 7.** Blind estimates of speckle variance for six-look real-life SAR images obtained by Method 2 and Method 3
