**5. Experimental results**

384 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

Fig. 10. Neighborhood cliques' organization for contourlet transforms

*H*, which are defined by

This approximation is possible, because all off-main diagonal elements represent covariances, and these are sparsely set matrixes that are close to zero, therefore those elements can be neglected. This assumption is in accordance with the statistical independence in Eq. (16). Only main-diagonal elements are needed for the Hessian matrix

1 1

 

1. The proposed despeckling algorithm transforms SAR images using bandelet (Le Pennec & Mallat, Apr 2005) or contourlet (da Cunha et al., 2006) transform. The number of decompositions depends on the size of the image. The number of levels *l* is chosen in such a way that the size of the approximation subband is larger than or equal to 64 × 64

2. The model parameters *ν* and *θ* are estimated inside a window with a size of *N* × *N*

5. The shape parameter *ν* is changed within the interval [0.5 … 2.5] with a step size of 0.1. 6. The noise-reduced coefficients are estimated using the MAP estimate (15) for each value *ν*. Each time, the texture parameters *θ* are estimated using the MAP estimate obtained in

*i i i n <sup>x</sup> h vv v v x x x*

*<sup>v</sup> <sup>N</sup> <sup>N</sup>*

<sup>ˆ</sup> 1, , <sup>ˆ</sup>

 (21)

 

2

pixels. In all experiments, a window with 7 × 7 pixels was used.

4. The parameter *θ* is estimated using the MMSE defined in (18).

3. The noise and signal variances are estimated using (13) and (14), respectively.

**4. Outline of the proposed algorithm** 

pixels (minimum size).

the previous step.

*ii x xi j i i*

  2

*j j i*

2
