Synthesis of adaptive weighted order statistic filters with gradient algorithms and application to image processing

This paper deals with the adaptive optimization of nonlinear weighted order statistic filters (WOSF). We propose three gradient-based approaches to adapt the filter weights and rank in order to minimize mean square and mean absolute error criteria. The two first solutions are derived from conventional gradient techniques, one solution uses an explicit formulation of the filter output while the second one results from an implicit formulation yet introduced to optimize rank order based filters. The third solution is derived from a three layer neural network scheme. Some practical examples illustrate the ability of the adaptive solutions to cope with texture restoration and noise removal in image processing