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A new approach to speckle reduction with texture preservation is presented termed granulometric shrinkage. The technique is analogous to wavelet shrinkage but with the wavelet transform replaced by a nonlinear multiscale granulometric sieve. The sieve employs area morphology, thus removing any shape bias associated with the use of fixed structuring elements. As the granulometric sieve is by nature edge preserving, the benefits of the new approach include improved edge and texture preservation. Experimental results using a SPOT image corrupted by synthetic speckle show the new approach to have a better speckle reduction capability than conventional wavelet shrinkage, with improved preservation of edges and other high frequency image features.