Nonstationary 2-D recursive restoration of images with signal-dependent noise

A nonstationary 2-D recursive image restoration filter that uses a nonstationary mean, nonstationary variance (NMNV) image model and minimizes the local mean square error is developed. The 2-D recursive filter adapts itself to the local image statistics and is able to do space-variant processing. The NMNV image model has a simple dynamic representation which simplifies the filter structure considerably. However, the optimal recursive filter still requires extensive computation. A suboptimal approach that uses a reduced update concept is proposed to reduce the computational efforts. With some modifications, this nonstationary 2-D recursive filter is extended to a class of uncorrelated, signal-dependent noise such as multiplicative noise and Poisson noise. The explicit filter structures and simulation results for images degraded by these signal-dependent noises are presented.