Nonstationary 2-D recursive filter for speckle reduction

Speckle noise exists in all types of coherent imagery such as synthetic aperture radar, acoustic imagery and laser illuminated imagery. Speckle can be reduced by averaging over several uncorrelated speckle images of the same object when these are available. In this paper, we attempt to reduce speckle noise from a single speckle image by using adaptive digital image restoration techniques. Many speckle noise reduction algorithms assume speckle noise is multiplicative. We model the speckle according the exact physical process of coherent image formation. Thus, the model includes signal-dependent effects and accurately represents the statistical properties of speckle. A linear minimum mean-square error filter is derived based on our speckle model and a nonstationary image model. The filter responds adaptively to the signal-dependent speckle noise and the nonstationary mean and variance of the original image. The necessary parameters are estimated from the noisy image. The 2-D recursive implementation of this filter is developed as a fast computation algorithm.