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Speckles appearing in synthetic aperture radar (SAR) images are generated by the coherent processing of radar signals. Basically the speckles have the nature of a multiplicative noise. A simple and effective method of smoothing speckle-corrupted images by a digital computer is discussed, based on the recently developed sigma filter. The sigma filter is motivated by the sigma probability of a Gaussian distribution. The pixel to be processed is replaced by an advantage of those neighboring pixels having their gray level within two noise standard deviations from that of the concerned pixel. Consequently the speckles are suppressed without blurring edges and fine detail. Several Seasat SAR images are used for illustration, and comparisons are made with several noise-smoothing algorithms. Extensions of this algorithm to contrast enhancement and signal-dependent noise filtering are also presented. This algorithm is computationally efficient, and has the potential to achieve real or near real-time processing.