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The undecimated wavelet transform and the maximum a posteriori probability (MAP) criterion have been applied to the problem of synthetic-aperture-radar image despeckling. The MAP solution is based on the assumption that wavelet coefficients have a known distribution. In previous works, the generalized Gaussian (GG) function has been successfully employed. Furthermore, despeckling methods can be improved by using a classification of wavelet coefficients according to their texture energy. A major drawback of using the GG distribution is the high computational cost since the MAP solution can be found only numerically. In this letter, a new modeling of the statistics of wavelet coefficients is proposed. Observations of the estimated GG shape parameters relative to the reflectivity and to the speckle noise suggest 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. As for the GG case, classification of wavelet coefficients according to their texture content may be exploited also in the proposed method. Experimental results show that the fast MAP estimator based on the Laplacian-Gaussian assumption and on the classification of coefficients reaches almost the same performances as the GG version in terms of speckle removal, with a gain in computational cost of about one order of magnitude.