Bayesian despeckling of SAR images based on Laplacian-Gaussian modeling of undecimated wavelet coefficients

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. In this case, a major problem is the computational cost, since the solution can be found only numerically. In this work, a different modeling is proposed. The observation of the experimental histograms of the wavelet coefficients related to the reflectivity and to speckle noise demonstrates that their distributions can be approximated as a Laplacian and a Gaussian function, respectively. Under these hypotheses, a closed form solution of the MAP estimation problem can be achieved. In addition, a closed form estimator based on the MMSE criterion also exists. The experimental results show that the fast MAP and MMSE estimators reach almost the same performances of their generalized Gaussian based counterparts in terms of speckle removal, with a computational gain of about one order of magnitude.