**1. Introduction**

Synthetic Aperture Radar (SAR) technology is mainly used to obtain high-resolution images of ground areas in resolutions even less than meter. SAR is even capable of imaging a wide area of terrain and from two and more images it is possible to reconstruct a 3D digital elevation model of ground terrain. Good thing about SAR is an all whether operation and possibility to capture images under various inclination angles. Because digital images are usually corrupted by noise that arises from an imaging device, there is always a need for a good filtering algorithm to remove all disturbances, thus enabling more information extraction. The SAR images are corrupted by a noise called speckle, which makes the interpretation of SAR images very difficult. The goal of removing speckles from the SAR image is to represent a noise-free image and preserve all important features of the SAR image, as for example edges, textures, region borders, etc.

Many different techniques for SAR image despeckling have been proposed over the past few years. Speckle is a noise-like characteristic of SAR images and it is a multiplicative nature, if the intensity or amplitude image is observed. The despeckling can be performed in the image or in the frequency domain. The well-known despeckling filters are Lee (Lee, 1980), Kuan (Kuan et al., 1985), and Frost (Frost et al., 1982). Lee and Kuan filters can be considered as an adaptive mean filters, meanwhile the Frost filter can be considered as a mean adaptive weighted filter. The Bayesian filters are based on the Bayesian theorem, which defines a posterior probability by using a prior, likelihood and evidence probability density functions (pdf). The solution for noise-free image is found by a maximum a posteriori (MAP) estimate. The MAP estimate of a noise free image was proposed in (Walessa & Datcu, 2000), where the noise free image was approximated by a Gauss-Markov random field prior and the noise was modeled with Gamma pdf. Model based despeckling and information extraction is one of the promising techniques of SAR image denoising and scene interpretation. The wavelet based despeckling algorithms have been proposed in (Dai et al., 2004), (Argenti & Alparone, 2002), and (Foucher et al., 2001). The second generation wavelets Chirplet (Cui & Wong, 2006), Contourlet (Chuna et al., 2006), Bandelet (Le Pennec & Mallat, Apr 2005) have appeared over the past few years.

Information Extraction and Despeckling of

**2. Second generation wavelets** 

results.

**2.1 Bandelets** 

different areas.

SAR Images with Second Generation of Wavelet Transform 375

is a band-pass image which is then led to directional filter bank where a directionality of an image is captured. This scheme can be further applied on a coarser image and thus an iterative scheme can be achieved. It can be concluded that applying iterative contourlet

For the despeckling of TerraSAR-X (Wikipedia, 2011) images we used a model based approach, which is supported by first order Bayesian inference. After applying transforms to images a general Gaussian distribution appears in wavelet domain. In this wavelet domain we get subbands different in scales and frequency. The subbands in the wavelet domain have Gaussian distribution and therefore the general Gaussian model is used for a prior density function (pdf). The likelihood pdf is modeled using Gaussian pdf in both, bandelet and contourlet transforms. The despeckling using contourlet (Li et al., 2006) and bandelet (Sveinsson et al., 2008) transforms showed superior despeckling results for SAR images comparing with the wavelet based methods. The model based despeckling mainly depends on chosen models. The image and noise models in the wavelet domain are well defined with presented results in (Argenti & Alparone, 2002), (Gleich & Datcu, 2006) and

The despeckling methods were tested using synthetic and real TerraSAR-X data, which were captured in the high resolution spotlight mode. The experimental results showed that the best despeckling method for synthetic images is bandelet transform, because contourlet transform produces artifacts in the homogenous areas. The ratio images between original and despeckled images were examined in order to show estimation of speckle noise, edge and texture preservation using bandelet and contourlet transform. The contourlet transform

In this section a comparison between bandelets and contourlets is presented. Bandelets and contourlets are presented in great detail, including subbands creation and filter decomposition. These two denoising schemes are a foundation of later proposed model, which builds a denoising scheme on top of these two schemes yielding better denoising

Bandelets (Le Pennec & Mallat, Apr 2005), (Le Pennec & Mallat, Dec 2005) belong to a second generation of wavelet transforms and are composed of anisotropic wavelets, which are in fact a combination of geometric flow of an image corresponding to local directions of its gray levels. This geometric flow represents a regularity of a vector field along edges contained in the image. Typical example of this geometric flow can be seen on Fig. 1, where it can be observed that all directions are aligned to object's edges at the boundary of two

Edges inside an image are often hard to determine. First generation of bandelet transform uses the vector field (Le Pennec & Mallat, 2001), which determines image regularities and irregularities. Therefore bandelet coefficients represent geometric flow defined by polynomial function. This geometric flow consists of directions of variations in image grey levels, where linear geometric flow is preferred. Bandelet transform image is divided into

scheme derives to directional subbands in a presence of multiple different scales.

usually noise-free image is computed using maximum a posteriori estimate.

produces artifacts in form of lines in both homogenous areas and edges.

First transform we used is so called Bandelet transform (Le Pennec & Mallat, Dec 2005), which further divides wavelet subbands into smaller subbands using a rate distortion optimization that enables removing redundancy in wavelet transformation. Bandelets (Le Pennec & Mallat, Dec 2005) contain anisotropic wavelets which combine redundancy in the geometric flow of an image corresponding to local directions of its grey levels. With this geometric flow wavelet warping represents a vector field with indication of regularity along edges. Bandelet decomposition is constructed in much the same way as wavelet with use of dyadic squares containing information about bandelet coefficients (parameterized geometric flow) and segmentation (Le Pennec & Mallat, Apr 2005). These squares summarize geometry by local clustering of similar directional vectors. A Bandelet transform can be viewed as an adaptive wavelet basis transform, which is warped according to local direction.

Bandelet transform is therefore capable to separate two different surface areas with different curvatures, which are then decomposed into optimal estimations of regularity direction (Le Pennec & Mallat, Apr 2005). The geometry itself is obtained with regularity flow estimation. Fig. 1 shows an example of directions acquired with bandelet transform. The computational complexity of this transform is much higher as in the case of the classical dyadic decomposition.

Fig. 1. Directions obtained by bandelet transform

The contourlet transform (Do & Vetterli, 2005) is organized a little bit different, because this transform is directly constructed in a discrete space. Thus, contourlet does not need to be transformed from continuous time-space domain. In order to capture as much as possible directional information a 2D directional filter bank is used in contourlet transform (Do & Vetterli, 2005). Directional filter bank is represented with *k*-binary tree which decomposes original image into 2*k* bands. These directional filter banks have a flaw mainly because they are designed to capture a direction, which is mainly done in high frequency spectrum of the input image, therefore low frequencies are obstructed. Low frequencies can easily penetrate into several different directional subbands, thus corrupting the transformation subbands. To solve this problem a multiscale decomposition is created with directional decomposition with the help of Laplacian pyramid as a low frequency filter. Laplacian pyramid throughput

First transform we used is so called Bandelet transform (Le Pennec & Mallat, Dec 2005), which further divides wavelet subbands into smaller subbands using a rate distortion optimization that enables removing redundancy in wavelet transformation. Bandelets (Le Pennec & Mallat, Dec 2005) contain anisotropic wavelets which combine redundancy in the geometric flow of an image corresponding to local directions of its grey levels. With this geometric flow wavelet warping represents a vector field with indication of regularity along edges. Bandelet decomposition is constructed in much the same way as wavelet with use of dyadic squares containing information about bandelet coefficients (parameterized geometric flow) and segmentation (Le Pennec & Mallat, Apr 2005). These squares summarize geometry by local clustering of similar directional vectors. A Bandelet transform can be viewed as an adaptive

Bandelet transform is therefore capable to separate two different surface areas with different curvatures, which are then decomposed into optimal estimations of regularity direction (Le Pennec & Mallat, Apr 2005). The geometry itself is obtained with regularity flow estimation. Fig. 1 shows an example of directions acquired with bandelet transform. The computational complexity of this transform is much higher as in the case of the classical dyadic

The contourlet transform (Do & Vetterli, 2005) is organized a little bit different, because this transform is directly constructed in a discrete space. Thus, contourlet does not need to be transformed from continuous time-space domain. In order to capture as much as possible directional information a 2D directional filter bank is used in contourlet transform (Do & Vetterli, 2005). Directional filter bank is represented with *k*-binary tree which decomposes original image into 2*k* bands. These directional filter banks have a flaw mainly because they are designed to capture a direction, which is mainly done in high frequency spectrum of the input image, therefore low frequencies are obstructed. Low frequencies can easily penetrate into several different directional subbands, thus corrupting the transformation subbands. To solve this problem a multiscale decomposition is created with directional decomposition with the help of Laplacian pyramid as a low frequency filter. Laplacian pyramid throughput

wavelet basis transform, which is warped according to local direction.

Fig. 1. Directions obtained by bandelet transform

decomposition.

is a band-pass image which is then led to directional filter bank where a directionality of an image is captured. This scheme can be further applied on a coarser image and thus an iterative scheme can be achieved. It can be concluded that applying iterative contourlet scheme derives to directional subbands in a presence of multiple different scales.

For the despeckling of TerraSAR-X (Wikipedia, 2011) images we used a model based approach, which is supported by first order Bayesian inference. After applying transforms to images a general Gaussian distribution appears in wavelet domain. In this wavelet domain we get subbands different in scales and frequency. The subbands in the wavelet domain have Gaussian distribution and therefore the general Gaussian model is used for a prior density function (pdf). The likelihood pdf is modeled using Gaussian pdf in both, bandelet and contourlet transforms. The despeckling using contourlet (Li et al., 2006) and bandelet (Sveinsson et al., 2008) transforms showed superior despeckling results for SAR images comparing with the wavelet based methods. The model based despeckling mainly depends on chosen models. The image and noise models in the wavelet domain are well defined with presented results in (Argenti & Alparone, 2002), (Gleich & Datcu, 2006) and usually noise-free image is computed using maximum a posteriori estimate.

The despeckling methods were tested using synthetic and real TerraSAR-X data, which were captured in the high resolution spotlight mode. The experimental results showed that the best despeckling method for synthetic images is bandelet transform, because contourlet transform produces artifacts in the homogenous areas. The ratio images between original and despeckled images were examined in order to show estimation of speckle noise, edge and texture preservation using bandelet and contourlet transform. The contourlet transform produces artifacts in form of lines in both homogenous areas and edges.
