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Speckle is a granular noise that inherently exists in all types of coherent imaging systems. The presence of speckle in an image reduces the resolution of the image and the detectability of the target. Many speckle reduction algorithms assume speckle noise is multiplicative. We instead model the speckle according to the exact physical process of coherent image formation. Thus, the model includes signal-dependent effects and accurately represents the higher order statistical properties of speckle that are important to the restoration procedure. Various adaptive restoration filters for intensity speckle images are derived based on different model assumptions and a nonstationary image model. These filters respond adaptively to the signal-dependent speckle noise and the nonstationary statistics of the original image.