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Synthetic Aperture Radar (SAR) Image despeckling is an important problem in SAR image processing since speckle may interfere with automatic interpretation. This paper presents a new approach for despeckling based on nonsubsampled shearlet transform. The approach introduced here presents two major contributions: (a) Translation-invariant Nonsubsampled Shearlet Transform (NSST) is designed to get more directional subbands which help to capture the anisotropic information of SAR image, and an estimation of speckle variance based on NSST is modeled to shrink NSST coefficients; (b) NSST coefficients are divided into several classes based on NSST- Multiscale Local Coefficient Variation (NSST-MLCV), which is helpful to reduce the undesired over-shrinkage, and shrinkage factor is obtained by computing the prior ratio and the likelihood ratio through mask. This model allows us to classify the NSST coefficients into classes having different degrees of heterogeneity, which can reduce the shrinkage ratio for heterogeneity regions while suppresses speckle effectively to realize both despeckling and detail preservation. Experimental results, carried out on both artificially speckled images and true SAR images, demonstrate that the proposed filtering approach outperforms the previous filters, irrespective of the features of the underlying reflectivity.