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In this letter, a texture-preserving despeckling algorithm for synthetic aperture radar images using an evidence framework is proposed. The salient aspects of this approach are given as follows. (1) The maximum a posteriori estimate can be guaranteed to converge to the optima by selecting the Gaussian distribution and Gaussian Markov random field model as the likelihood function and prior model, respectively. (2) MacKay's evidence framework can automatically sustain the balance between speckle reduction and texture preservation. (3) We use the Jeffreys prior to perform the second-level inference of the evidence framework. Experimental results are given to demonstrate the validity of the proposed despeckling method.