**5.1 Synthetic SAR images**

The synthetic SAR image, shown in Fig. 11, is composed of four different areas and with added four-look multiplicative speckle noise. The SAR image size shown in Fig. 11 is 512 × 512 pixels; therefore three levels of decomposition are used for bandelet transform. First let us show the difference between the pure bandelet and contourlet, and the MBD method.

Fig. 11. a) Original speckled image, b) Despeckled image obtained with the original bandelet denoising scheme, c) Despeckled image obtained with the original contourlet denoising scheme, and d) Despeckled image obtained with the MBD denoising technique

Information Extraction and Despeckling of

reported in Table 1.

with the MBD method

Table 1. Filter evaluation for synthetic test images

but it overblurs the reconstructed image, yielding a worse MSE value.

SAR Images with Second Generation of Wavelet Transform 387

*μ = 127.94 Bandelet Contourlet MBD*  MSE 331 447 463 Mean 127.64 127.4 126.49 ENL ( *x*ˆ ) 506 510 539 ENL (y/ *x*ˆ ) 3.14 3.2 3.18 Mean (y/ *x*ˆ ) 1.047 1.048 0.94

In Table 1, the objective measurements are presented for the denoising of image shown in Fig. 12. Objective measurements include the mean-square error (MSE), the equivalent number of looks (ENL), the mean value of the despeckled image, the ENL of speckle noise (ENL(y/ *x*ˆ )), and the mean value of speckle noise y/ *x*ˆ . The ENL of the image is given by μ2/σ2. The best MSE results are from bandelet transform in combination with Bayesian inference, thus having better results than those obtained from the contourlet transforms. A drawback of the contourlet transform is that it produces contours in the reconstructed image, which affects a MSE value. All wavelet-based methods well preserve the mean of the despeckled images. On the other hand, the MBD method well estimates the speckle noise,

Figs. 13 a)-c) show the ratio images between the original and the reconstructed mosaic images obtained with bandelet, contourlet, and MDB. From these ratio images we can conclude that edges are well preserved, and that the speckle noise in the homogeneous areas is well estimated (i.e. removed) using the MBD method and second generation wavelets, as

a) b) c) Fig. 13. Ratio images y/ *x*ˆ . a) Ratio image obtained with the bandelet-based despeckling, b) Ratio image obtained with the countourlet-based despeckling, and c) Ratio image obtained

The efficiency of the texture separation regarding the proposed method is demonstrated on four Brodatz textures, which are presented in a single mosaic composition and shown in Fig. 14. The textures are corrupted with a four-look speckle noise. The estimated parameter *θ2* obtained from bandelet and contourlet transforms is shown in Fig. 14 b) and

The bandelet transform is composed of a larger sliding window with a size of 16 × 16 (i.e. moving window per window), meanwhile inside a larger window, a smaller one with the size of 4 × 4 pixels moves on pixel basis. Those two sliding windows are used for searching the best decomposition inside the dyadic wavelet transform (Le Pennec & Mallat, Apr 2005). The contourlet transform is constructed using eight directions at the first level of decomposition. The last two levels are chosen to be dyadic, but this is not a requirement. The despeckled images obtained using the bandelet and contourlet transform are shown in Fig. 11 b) and c), respectively. Moreover, the despeckled image obtained using the MBD (Walessa & Datcu, 2000) is shown in Fig. 11 d).

And now with the MAP incorporated into the bandelet and contourlet transform.

Fig. 12. a) Original speckled image, b) Despeckled image obtained with the bandeleted denoising scheme, c) Despeckled image obtained with the contourlet denoising scheme, and d) Despeckled image obtained with the MBD denoising technique

The bandelet transform is composed of a larger sliding window with a size of 16 × 16 (i.e. moving window per window), meanwhile inside a larger window, a smaller one with the size of 4 × 4 pixels moves on pixel basis. Those two sliding windows are used for searching the best decomposition inside the dyadic wavelet transform (Le Pennec & Mallat, Apr 2005). The contourlet transform is constructed using eight directions at the first level of decomposition. The last two levels are chosen to be dyadic, but this is not a requirement. The despeckled images obtained using the bandelet and contourlet transform are shown in Fig. 11 b) and c), respectively. Moreover, the despeckled image obtained using the MBD

a) b)

c) d)

Fig. 12. a) Original speckled image, b) Despeckled image obtained with the bandeleted denoising scheme, c) Despeckled image obtained with the contourlet denoising scheme, and

d) Despeckled image obtained with the MBD denoising technique

And now with the MAP incorporated into the bandelet and contourlet transform.

(Walessa & Datcu, 2000) is shown in Fig. 11 d).



In Table 1, the objective measurements are presented for the denoising of image shown in Fig. 12. Objective measurements include the mean-square error (MSE), the equivalent number of looks (ENL), the mean value of the despeckled image, the ENL of speckle noise (ENL(y/ *x*ˆ )), and the mean value of speckle noise y/ *x*ˆ . The ENL of the image is given by μ2/σ2. The best MSE results are from bandelet transform in combination with Bayesian inference, thus having better results than those obtained from the contourlet transforms. A drawback of the contourlet transform is that it produces contours in the reconstructed image, which affects a MSE value. All wavelet-based methods well preserve the mean of the despeckled images. On the other hand, the MBD method well estimates the speckle noise, but it overblurs the reconstructed image, yielding a worse MSE value.

Figs. 13 a)-c) show the ratio images between the original and the reconstructed mosaic images obtained with bandelet, contourlet, and MDB. From these ratio images we can conclude that edges are well preserved, and that the speckle noise in the homogeneous areas is well estimated (i.e. removed) using the MBD method and second generation wavelets, as reported in Table 1.

Fig. 13. Ratio images y/ *x*ˆ . a) Ratio image obtained with the bandelet-based despeckling, b) Ratio image obtained with the countourlet-based despeckling, and c) Ratio image obtained with the MBD method

The efficiency of the texture separation regarding the proposed method is demonstrated on four Brodatz textures, which are presented in a single mosaic composition and shown in Fig. 14. The textures are corrupted with a four-look speckle noise. The estimated parameter *θ2* obtained from bandelet and contourlet transforms is shown in Fig. 14 b) and

Information Extraction and Despeckling of

SAR Images with Second Generation of Wavelet Transform 389

decomposition. Five levels of contourlet transform are used, where the last two decompositions are dyadic and all other levels are contourlet directional subbunds consisted of eight directional subbands. The Daubechies symmetric four-filter bank (Daubechies, 1992)

a) b)

c) d) Fig. 15. a) Original TerraSAR-X image © DLR (2007), b) Despeckled image obtained with the bandelet transform, c) Despeckled image obtained with the contourlet transforms, and

d) Despeckled image obtained with the MBD method

is used for the construction of bandelet and contourlet transforms.

c), respectively. The estimated texture parameters *θ* are classified into four classes using the *K*-means algorithm, and the classification results are shown in Fig. 14 d) and e), respectively. The best texture separation is obtained using a contourlet transform. The unsupervised classification of the texture parameters has an accuracy rate of 82 % and 89 %, for texture parameters obtained from the bandelet and contourlet transforms, respectively. Fig. 14 f) shows the classification of the texture parameter *θ* obtained with the MBD method. This method cannot well estimate classes on the right side of the image shown in Fig. 14 f).

Fig. 14. a) Brodatz textures composed into a mosaic image, b) Texture parameter *θ<sup>2</sup>* obtained with the bandelet transform, c) Texture parameter *θ2* obtained with the contourlet transform, d) Classified parameter *θ* obtained with the bandelet transform using the *K*-means unsupervised classification into four classes, e) Classified parameter *θ* obtained with the contourlet transform using the *K*-means unsupervised classification into four classes, and f) Classified parameter *θ* obtained with the MBD method and *K*-means unsupervised classification into four classes

#### **5.2 Real SAR images**

The real SAR images are a sample images taken by TerraSAR-X satellite. The amplitude part of a single-look complex (SLC) SAR image is shown in Fig. 15 with a size of 2048×2048 pixels and ENL equal to 1.1. Four levels of dyadic decomposition are used for the bandelet

c), respectively. The estimated texture parameters *θ* are classified into four classes using the *K*-means algorithm, and the classification results are shown in Fig. 14 d) and e), respectively. The best texture separation is obtained using a contourlet transform. The unsupervised classification of the texture parameters has an accuracy rate of 82 % and 89 %, for texture parameters obtained from the bandelet and contourlet transforms, respectively. Fig. 14 f) shows the classification of the texture parameter *θ* obtained with the MBD method. This method cannot well estimate classes on the right side of the image

a) b) c)

d) e) f)

obtained with the bandelet transform, c) Texture parameter *θ2* obtained with the contourlet transform, d) Classified parameter *θ* obtained with the bandelet transform using the *K*-means unsupervised classification into four classes, e) Classified parameter *θ* obtained with the contourlet transform using the *K*-means unsupervised classification into four classes, and f) Classified parameter *θ* obtained with the MBD method and *K*-means

The real SAR images are a sample images taken by TerraSAR-X satellite. The amplitude part of a single-look complex (SLC) SAR image is shown in Fig. 15 with a size of 2048×2048 pixels and ENL equal to 1.1. Four levels of dyadic decomposition are used for the bandelet

Fig. 14. a) Brodatz textures composed into a mosaic image, b) Texture parameter *θ<sup>2</sup>*

unsupervised classification into four classes

**5.2 Real SAR images** 

shown in Fig. 14 f).

decomposition. Five levels of contourlet transform are used, where the last two decompositions are dyadic and all other levels are contourlet directional subbunds consisted of eight directional subbands. The Daubechies symmetric four-filter bank (Daubechies, 1992) is used for the construction of bandelet and contourlet transforms.

c) d)

Fig. 15. a) Original TerraSAR-X image © DLR (2007), b) Despeckled image obtained with the bandelet transform, c) Despeckled image obtained with the contourlet transforms, and d) Despeckled image obtained with the MBD method

Information Extraction and Despeckling of

iterations.

transform subbands

these methods are also computationally comparable.

SAR Images with Second Generation of Wavelet Transform 391

The despeckling within the bandelet and dyadic wavelet domain are able to remove speckles around the strong scatterers, while the contourlet transform produces artifacts in this configuration. Higher image values are difficult to despeckle, because of the nature of the contourlet transform. Therefore, the noise is still present in those areas of the reconstructed image. However, the bandelet transform is overall computationally more demanding than contourlet transform (around 5.6 times), yet the despeckling of each contourlet subband takes about 4.5 times longer than with bandelet transform. Therefore,

To extract texture information from the denoised TerraSAR-X images we have used General Gauss-Markov Random Fields (GGMRF) as a prior pdf (Gleich & Datcu, 2007). As a prior pdf a first order model was used with cliques defined as Gauss-Markov Random Fields and shown in Figs. 9 and 10. Cliques were used to estimate central pixels for both transforms created in a 7 × 7 window which is moving throughout the whole picture. This was applied on transform's first approximation and its corresponding subbands. The texture parameters are iteratively estimated until second order Bayesian inference is increasing, which is used for finding the best model (Gleich & Datcu, 2007). The results of this method can be seen in Fig. 18, where the classification parameters for *K*-means algorithm were 5 classes and 7

a) b) c)

Texture parameters *θ* obtained during the despeckling procedure of the SAR image shown in Fig. 15 with bandelet, contourlet, and MBD method are shown in Fig. 19 b)-d). The algorithm used for classification into four different classes is the *K*-means algorithm. Fig. 19 a) is an indication of *K*-means algorithm applied to original image scene, where no textures can be identified as no processing was applied. The texture parameters obtained with both proposed algorithms clearly separate between homogeneous and heterogeneous areas. The contourlet transform compared to bandelet transform better separates the homogeneous and heterogeneous areas. From images it can be concluded, that contourlet transform is able to separate more heterogeneous areas from homogeneous ones. As a comparison, the MBD

Fig. 18. Comparison on information extraction. A) Original TerraSAR-X© image, b) Classified image on bandelet transform subbands, and c) Classified image on contourlet

Fig. 15 a)-d) shows the original SLC SAR image and the despeckled images obtained using the bandelet- and contourlet-based despeckling techniques, and the MBD despeckling method. Their ratio images are shown in Fig. 16 a)-c). The quality of the reconstructed images using the bandelet and contourlet transforms is nearly the same. However, the despeckling method based on bandelet transform has left out some speckle noise in the homogeneous regions. On the other hand, the homogeneous regions are well despeckled in the reconstructed image based on the contourlet transform, but undesired artifacts emerge in places around strong scatter returns in shape of lines, that are a consequence of contourlet subbands decomposition. This artifact is clearly visible in Fig. 16 b). Figs. 17 a)-c) show how strong scatterers are despeckled within the bandelet, contourlet, and dyadic wavelet domain.

Fig. 16. Ratio images y/ *x*ˆ for SAR images. a) Ratio image obtained with the bandelet transform, b) Ratio image obtained with contourlet transform, and c) Ratio image obtained with the MBD method

a) b) c)

a) b) c)

Fig. 17. Despeckling of strong scatterers using a) bandelet transform, b) contourlet transform, and c) MBD method

Fig. 15 a)-d) shows the original SLC SAR image and the despeckled images obtained using the bandelet- and contourlet-based despeckling techniques, and the MBD despeckling method. Their ratio images are shown in Fig. 16 a)-c). The quality of the reconstructed images using the bandelet and contourlet transforms is nearly the same. However, the despeckling method based on bandelet transform has left out some speckle noise in the homogeneous regions. On the other hand, the homogeneous regions are well despeckled in the reconstructed image based on the contourlet transform, but undesired artifacts emerge in places around strong scatter returns in shape of lines, that are a consequence of contourlet subbands decomposition. This artifact is clearly visible in Fig. 16 b). Figs. 17 a)-c) show how strong scatterers are despeckled within the bandelet, contourlet, and dyadic wavelet domain.

a) b) c)

a) b) c)

Fig. 17. Despeckling of strong scatterers using a) bandelet transform, b) contourlet

Fig. 16. Ratio images y/ *x*ˆ for SAR images. a) Ratio image obtained with the bandelet transform, b) Ratio image obtained with contourlet transform, and c) Ratio image obtained

with the MBD method

transform, and c) MBD method

The despeckling within the bandelet and dyadic wavelet domain are able to remove speckles around the strong scatterers, while the contourlet transform produces artifacts in this configuration. Higher image values are difficult to despeckle, because of the nature of the contourlet transform. Therefore, the noise is still present in those areas of the reconstructed image. However, the bandelet transform is overall computationally more demanding than contourlet transform (around 5.6 times), yet the despeckling of each contourlet subband takes about 4.5 times longer than with bandelet transform. Therefore, these methods are also computationally comparable.

To extract texture information from the denoised TerraSAR-X images we have used General Gauss-Markov Random Fields (GGMRF) as a prior pdf (Gleich & Datcu, 2007). As a prior pdf a first order model was used with cliques defined as Gauss-Markov Random Fields and shown in Figs. 9 and 10. Cliques were used to estimate central pixels for both transforms created in a 7 × 7 window which is moving throughout the whole picture. This was applied on transform's first approximation and its corresponding subbands. The texture parameters are iteratively estimated until second order Bayesian inference is increasing, which is used for finding the best model (Gleich & Datcu, 2007). The results of this method can be seen in Fig. 18, where the classification parameters for *K*-means algorithm were 5 classes and 7 iterations.

Fig. 18. Comparison on information extraction. A) Original TerraSAR-X© image, b) Classified image on bandelet transform subbands, and c) Classified image on contourlet transform subbands

a) b) c)

Texture parameters *θ* obtained during the despeckling procedure of the SAR image shown in Fig. 15 with bandelet, contourlet, and MBD method are shown in Fig. 19 b)-d). The algorithm used for classification into four different classes is the *K*-means algorithm. Fig. 19 a) is an indication of *K*-means algorithm applied to original image scene, where no textures can be identified as no processing was applied. The texture parameters obtained with both proposed algorithms clearly separate between homogeneous and heterogeneous areas. The contourlet transform compared to bandelet transform better separates the homogeneous and heterogeneous areas. From images it can be concluded, that contourlet transform is able to separate more heterogeneous areas from homogeneous ones. As a comparison, the MBD

Information Extraction and Despeckling of

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SAR Images with Second Generation of Wavelet Transform 393

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Fig. 19. Classification of texture parameter *θ* using the *K*-means algorithm and the a) original, b) bandelet, c) contourlet, and d) MBD-based algorithm
