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Speckle filter performance depends strongly on the speckle and scene models used as the basis for filter development. These models implicitly incorporate certain assumptions about speckle, scene, and observed signals. In this study, the multiplicative and the product speckle models, which have been used for the development of most of the well-known filters, are analyzed, and their implicit assumptions with regard to the stationarity-nonstationarity nature of speckle are discussed. This leads to the definition of two categories of speckle filters: the stationary and the nonstationary multiplicative speckle model filters. The various approximate models used for the multiplicative speckle noise model are assessed as functions of speckle and scene characteristics to derive the requirements on scene signal variations for the validity of both the stationary and nonstationary multiplicative speckle models. Speckle filtering is then studied in the context of estimation theory, so as to develop a procedure for speckle filtering. It is shown that speckle filtering can be effective only in locally stationary scenes. Regions in which the signals are not stationary have to be filtered separately using a priori scene templates for the best matching of nonstationary scene features. The use of multiresolution techniques is crucial for accurate estimation of filter parameters. Under the guidance of the speckle filtering procedure, structural-multiresolution versions of the Lee (1980) and Frost et al. (1982) filters are developed for optimum application of these filters in the context of nonstationary scene signals.