The undecimated wavelet transform and the maximum a posteriori (MAP) criterion have been applied to the problem of despeckling SAR images. The solution is based on the assumption that the wavelet coefficients have a known distribution; in previous works, the generalized Gaussian function has been successfully employed. Furthermore, despeckling methods can be improved by using a classification of the wavelet coefficients according to their texture energy. A major drawback of using the generalized Gaussian distribution is the high computational cost, since the MAP solution can be found only numerically. In this work, a new modeling of the statistics of the wavelet coefficients is proposed. The observation of the experimental estimated generalized Gaussian shape parameters related to the reflectivity and to speckle noise suggests that their distributions can be approximated as a Laplacian and as a Gaussian function, respectively. Under these hypotheses, a closed form solution of the MAP estimation problem can be achieved. As for the generalized Gaussian case, classification of the wavelet coefficients according to their texture content can also be exploited in the new proposed method. The experimental results show that the fast MAP estimator based on the Laplacian-Gaussian assumption and on coefficient classification reaches almost the same performances of the generalized Gaussian counterpart in terms of speckle removal, with a computational gain of about one order of magnitude.
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