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A novel adaptive median filter is proposed. It allows the simultaneous removal of a combination of signal-dependent and additive random noise in addition to mixed impulse noise in images, processed in a single filtering pass. The adaptation algorithm is based on the local signal-to-noise ratio. An extension of the class of nonlinear mean filters to adaptive filters is considered. The performance of the adaptive median filter is compared to the commonly used median filter and the nonlinear mean filter.