Adaptive and global optimization methods for weighted vector median filters

Abstract Weighted vector median filters (WVMF) are a powerful tool for the non-linear processing of multi-components signals. These filters are parametrized by a set of N weights and, in this paper, we propose two optimization techniques of these weights for colour image processing. The first one is an adaptive optimization of the N−1 peripheral weights of the filter mask. The major and more difficult task is to get a mathematical expression for the derivative of the WVMF output with respect to its weights; two approximations are proposed to measure this filter output sensitivity. The second optimization technique corresponds to a global optimization of the central weight alone, the value of which is determined, in a noise reduction context, by an analytical expression depending upon the mask size and the probability of occurrence of an impulsive noise. Both approaches are evaluated by simulations related to the denoising of textured, or natural, colour images, in the presence of impulsive noise. Furthermore, as they are complementary, they are also tested when used together.