**1. Introduction**

20 Computational and Numerical Simulations

302 Computational and Numerical Simulations

2008

Neurocomputing 71, pp 1500-1514, 2008

by IEEE Trans. on Neural Networks, 2008

network," Applied Soft Computing 2005; 5:333–355

model," Neurocomputing 50 (2003) 159 – 175.

[16] J. M. Wu, "Fetal electrocardiogram extraction by annealed expectation maximization,"

[17] J. M. Wu, "Multilayer Potts perceptrons with Levenberg-Marquardt learning", accepted

[18] J. M. Wu, M.H. Chen, Lin Z.H., "Independent component analysis based on marginal density estimation using weighted Parzen windows", accepted by Neural Networks,

[19] Dudul SV, "Prediction of Lorenz chaotic attractor using two layer perceptron neural

[20] G. Peter Zhang, "Time series forecasting using a hybrid ARIMA and neural network

Blind estimation of noise characteristics (BENC), such as noise type, its statistics and spectrum, has become an actual practical task for various image processing applications (Vozel et al., 2009). There are several reasons for this. First, noise is one of the main factors degrading and determining the quality of images of different types: grayscale and color optical (Liu et al., 2008; Foi et al., 2007; Plataniotis&Venetsanopoulos, 2000), component images in certain subbands of hyperspectral remote sensing data (Aiazzi et al., 2006), radar and ultrasound medical images (Lin et al., 2010; Oliver&Quegan, 2004), etc. Second, information on noise characteristics is valuable and widely exploited in most of stages of image processing. For example, it is used in edge detection for threshold setting (Davies, 2000), image filtering (Touzi, 2002; Lee et al., 2009) including denoising techniques based on orthogonal transforms (Mallat, 1998; Sen‐ dur&Selesnick, 2002; Egiazarian et al., 1999), image reconstruction (Katsaggelos, 1991), lossy compression of noisy images (Bekhtin, 2011), non-reference assessment of image visual quality (Choi et al., 2009), etc. Third, although there can be initial assumptions on noise type and a range of variations of its statistical parameters, these parameters can be quite different even for a given imaging system depending upon conditions of its operation. The requirements to information accuracy on noise parameters are rather strict, e.g., variance of pure additive or pure multiplicative noise has to be known or pre-estimated with a relative error not larger than ±20% (Abramov et al., 2004). Thus, it is often desirable to estimate noise characteristics for a given image.

© 2014 Abramov et al.; licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Besides, amount of images offered by various imaging systems increases enormously. Therefore, it becomes difficult to evaluate noise characteristics in an interactive manner since this requires time, perfect skills, and availability of the corresponding software. Moreover, there are practical situations and applications for which it is impossible to find a highly qualified expert to perform the task of evaluation of the noise characteristics. The examples are estimation of noise characteristics in remote sensing images on-board satellites (Van Zyl et al., 2009). BENC can be also useful even if an expert is involved to analysis of the noise characteristics. This happens, e.g., if a newly designed and manufactured imaging system is verified to check do the main properties of the noise present in the formed images conform expected (forecasted) ones. Then, the output estimates of BENC can be compared to the outcomes of the expert analysis and support (control) each other.

al., 1992; Ramponi&d'Alvise, 1999). Third, although it is assumed that the multi-look mode of image formation allows decreasing the speckle variance by the number of looks, this is not absolutely true and, in practice, noise reduction is not as efficient as ideally predicted (Anfinsen

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

305

Therefore, two important questions arise: what is the accuracy of the existing blind estimation methods and what BENC to apply? To our best knowledge, there are no studies dealing with intensive testing of BENC with application to speckle (our conference paper (Lukin et al., 2011) seems to be one of the first attempts in this direction). By intensive testing we mean the use of tens of different images having different content and/or many realizations of speckle for both single and multi-look modes. There are several reasons why such testing has not been carried out yet. The main reason is the absence of the test radar images commonly accepted by the radar data processing community. We have to stress here that it is quite difficult to create test SAR images since one has to find an answer to many particular questions as what terrain and objects to simulate, what model of the carrier trajectory and its instabilities to use, to consider moving objects or not, what is SNR in radar receiver input, what kind of received signal processing is used (Dogan&Kartal, 2010; Di Martino et al., 2012), etc. Another reason is that, maybe, designers of BENC for speckle have been satisfied by accuracy of the obtained estimates for a limited set of processed images and have not tried applying their methods to

Experience obtained recently in testing BENCs for additive and signal dependent noise cases (Vozel et al., 2009; Abramov et al., 2011; Lukin et al., 2009b) clearly demonstrates the following. First, whilst a given method can produce an acceptable accuracy for many tested images, there can be a few test images (usually highly textural ones and/or with clipping effects) for which abnormal (unacceptable) estimates are obtained. Just to these images one has to pay more attention in attempts to improve a methods' performance. Second, a spatial correlation of noise present in most of real life images and often ignored in a design and testing of many BENC techniques can considerably influence an accuracy of estimation methods (Abramov et al., 2008). Recall that a spatial correlation of speckle is a feature typical for SAR images (Solbo&El‐ toft, 2008, Lukin et al., 2008; Lukin et al., 2009; Ponomarenko et al., 2011) which is not often

Thus, we come to a necessity to perform intensive testing of BENC methods without having a set of standard test images. Our idea then is to create a set of test SAR images with a priori known characteristics of the speckle similar to those ones observed in practice. In this sense, TerraSAR-X images can be a good choice (in Section 2, we explain this in detail). Note that quite many of them are now available in the convenient form and their amount is rapidly growing (see http://www.infoterra.de/free-sample-data). Then, it becomes possible to test BENCs for simulated data (Section 3) and to predict what could happen in practice. These predictions are then verified for the considered methods for high quality data provided by TerraSAR-X data (Section 4) to offer practical recommendations on the BENC method selection

et al., 2009; Foucher et al., 2000).

a wider variety of data.

taken into account in SAR image simulations.

and setting its parameters. Finally, conclusions follow.

There are quite many known methods of BENC designed so far. A few of them can operate on images corrupted by a general type of signal-dependent noise (Liu et al., 2008). Most of known BENC methods are able to deal only with a particular type of noise under assumption that the noise type is known a priori or pre-determined in an automatic manner (Vozel et al., 2009). The case of pure additive noise has been studied more thoroughly in literature (see Vozel et al. 2009; Zoran&Weiss, 2009; Abramov et al., 2008; Lukin et al. 2007, and references therein). Some of these methods can be, after certain modifications, applied to estimation of multipli‐ cative noise variance. These modifications basically relate to either application of logarithmic type homomorphic transform or a special approach to form local estimates of multiplicative noise relative variance as a normalization of local variance estimates by squared local mean (Vozel et al. 2009). However, quite many BENC methods exploit local estimate scatter-plots and line (curve) fitting into them to evaluate multiplicative noise variance (Lee et al., 1992; Ramponi&d'Alvise, 1999). Note that a multiplicative noise is typical for radar imagery, in particular, images acquired by synthetic aperture radars (SARs) where coherent principles of image forming are employed (Solbo&Eltoft, 2004; Oliver&Quegan, 2004). Speckle is a specific noise-like phenomenon arising in formed images and it is known to be the dominant factor degrading their quality (Oliver&Quegan, 2004). For many operations of radar (and ultrasound) image processing, the characteristics of the speckle are to be known in advance or preestimated (Lee et al., 2009; Solbo&Eltoft, 2008).

One can argue that there are many practical situations when speckle characteristics such as the (relative) variance of the multiplicative noise (or the efficient number of looks) and the speckle distribution law are known in advance or can be predicted from theory (Oliver&Que‐ gan, 2004). This holds if a given SAR operates in a known mode (e.g. forms one-look amplitude images) and the operation parameters are stable. Then, it is enough to carry out a preliminary analysis of several images acquired by this SAR manually (in interactive mode) to be sure that the aforementioned characteristics (parameters) conform theory and are stable enough.

However, in many practical situations, it is worth applying BENC, sometimes in addition to an interactive analysis. First, suppose that a new SAR is tested and it is desirable to know whether or not it provides the desired (forecasted, expected) characteristics. Second, one might deal with SAR images for which full description of the imaging mode used is absent (Lee et al., 1992; Ramponi&d'Alvise, 1999). Third, although it is assumed that the multi-look mode of image formation allows decreasing the speckle variance by the number of looks, this is not absolutely true and, in practice, noise reduction is not as efficient as ideally predicted (Anfinsen et al., 2009; Foucher et al., 2000).

Besides, amount of images offered by various imaging systems increases enormously. Therefore, it becomes difficult to evaluate noise characteristics in an interactive manner since this requires time, perfect skills, and availability of the corresponding software. Moreover, there are practical situations and applications for which it is impossible to find a highly qualified expert to perform the task of evaluation of the noise characteristics. The examples are estimation of noise characteristics in remote sensing images on-board satellites (Van Zyl et al., 2009). BENC can be also useful even if an expert is involved to analysis of the noise characteristics. This happens, e.g., if a newly designed and manufactured imaging system is verified to check do the main properties of the noise present in the formed images conform expected (forecasted) ones. Then, the output estimates of BENC can be compared to the

There are quite many known methods of BENC designed so far. A few of them can operate on images corrupted by a general type of signal-dependent noise (Liu et al., 2008). Most of known BENC methods are able to deal only with a particular type of noise under assumption that the noise type is known a priori or pre-determined in an automatic manner (Vozel et al., 2009). The case of pure additive noise has been studied more thoroughly in literature (see Vozel et al. 2009; Zoran&Weiss, 2009; Abramov et al., 2008; Lukin et al. 2007, and references therein). Some of these methods can be, after certain modifications, applied to estimation of multipli‐ cative noise variance. These modifications basically relate to either application of logarithmic type homomorphic transform or a special approach to form local estimates of multiplicative noise relative variance as a normalization of local variance estimates by squared local mean (Vozel et al. 2009). However, quite many BENC methods exploit local estimate scatter-plots and line (curve) fitting into them to evaluate multiplicative noise variance (Lee et al., 1992; Ramponi&d'Alvise, 1999). Note that a multiplicative noise is typical for radar imagery, in particular, images acquired by synthetic aperture radars (SARs) where coherent principles of image forming are employed (Solbo&Eltoft, 2004; Oliver&Quegan, 2004). Speckle is a specific noise-like phenomenon arising in formed images and it is known to be the dominant factor degrading their quality (Oliver&Quegan, 2004). For many operations of radar (and ultrasound) image processing, the characteristics of the speckle are to be known in advance or pre-

One can argue that there are many practical situations when speckle characteristics such as the (relative) variance of the multiplicative noise (or the efficient number of looks) and the speckle distribution law are known in advance or can be predicted from theory (Oliver&Que‐ gan, 2004). This holds if a given SAR operates in a known mode (e.g. forms one-look amplitude images) and the operation parameters are stable. Then, it is enough to carry out a preliminary analysis of several images acquired by this SAR manually (in interactive mode) to be sure that the aforementioned characteristics (parameters) conform theory and are stable enough.

However, in many practical situations, it is worth applying BENC, sometimes in addition to an interactive analysis. First, suppose that a new SAR is tested and it is desirable to know whether or not it provides the desired (forecasted, expected) characteristics. Second, one might deal with SAR images for which full description of the imaging mode used is absent (Lee et

outcomes of the expert analysis and support (control) each other.

304 Computational and Numerical Simulations

estimated (Lee et al., 2009; Solbo&Eltoft, 2008).

Therefore, two important questions arise: what is the accuracy of the existing blind estimation methods and what BENC to apply? To our best knowledge, there are no studies dealing with intensive testing of BENC with application to speckle (our conference paper (Lukin et al., 2011) seems to be one of the first attempts in this direction). By intensive testing we mean the use of tens of different images having different content and/or many realizations of speckle for both single and multi-look modes. There are several reasons why such testing has not been carried out yet. The main reason is the absence of the test radar images commonly accepted by the radar data processing community. We have to stress here that it is quite difficult to create test SAR images since one has to find an answer to many particular questions as what terrain and objects to simulate, what model of the carrier trajectory and its instabilities to use, to consider moving objects or not, what is SNR in radar receiver input, what kind of received signal processing is used (Dogan&Kartal, 2010; Di Martino et al., 2012), etc. Another reason is that, maybe, designers of BENC for speckle have been satisfied by accuracy of the obtained estimates for a limited set of processed images and have not tried applying their methods to a wider variety of data.

Experience obtained recently in testing BENCs for additive and signal dependent noise cases (Vozel et al., 2009; Abramov et al., 2011; Lukin et al., 2009b) clearly demonstrates the following. First, whilst a given method can produce an acceptable accuracy for many tested images, there can be a few test images (usually highly textural ones and/or with clipping effects) for which abnormal (unacceptable) estimates are obtained. Just to these images one has to pay more attention in attempts to improve a methods' performance. Second, a spatial correlation of noise present in most of real life images and often ignored in a design and testing of many BENC techniques can considerably influence an accuracy of estimation methods (Abramov et al., 2008). Recall that a spatial correlation of speckle is a feature typical for SAR images (Solbo&El‐ toft, 2008, Lukin et al., 2008; Lukin et al., 2009; Ponomarenko et al., 2011) which is not often taken into account in SAR image simulations.

Thus, we come to a necessity to perform intensive testing of BENC methods without having a set of standard test images. Our idea then is to create a set of test SAR images with a priori known characteristics of the speckle similar to those ones observed in practice. In this sense, TerraSAR-X images can be a good choice (in Section 2, we explain this in detail). Note that quite many of them are now available in the convenient form and their amount is rapidly growing (see http://www.infoterra.de/free-sample-data). Then, it becomes possible to test BENCs for simulated data (Section 3) and to predict what could happen in practice. These predictions are then verified for the considered methods for high quality data provided by TerraSAR-X data (Section 4) to offer practical recommendations on the BENC method selection and setting its parameters. Finally, conclusions follow.
