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We first establish a law of large numbers and a convergence theorem indistribution to show the rate of convergence of the non-local means filter forremoving Gaussian noise. We then introduce the notion of degree of similarityto measure the role of similarity for the non-local means filter. Based on theconvergence theorems, we propose a patch-based weighted means filter forremoving impulse noise and its mixture with Gaussian noise by combining theessential idea of the trilateral filter and that of the non-local means filter.Our experiments show that our filter is competitive compared to recentlyproposed methods.

Removing Mixture of Gaussian and Impulse Noise by Patch-Based Weighted Means