Adaptive Weighted Myriad Filter Optimization for Robust Signal Processing

| Weighted Myriad Filters have been proposed recently as a class of robust, nonlinear lters based on the statistical properties of-stable processes. These processes are very eeective in modeling many real-world signals that are impulsive in nature. The class of Weighted Myriad Filters includes linear normalized FIR lters and is inherently more powerful than weighted median lters (which are constrained to be selection lters). This paper addresses the problem of optimizing the weights of the weighted myriad lter under the mean absolute error criterion. Necessary conditions for optimality of the lter are determined. Using an implicit formulation of the lter output, a gradient-based adaptive algorithm to obtain the optimal lter weights is derived. A simpliication of this algorithm is then proposed in order to reduce the computational burden. The eeective performance of the algorithms in impulsive environments is illustrated through computer simulations involving the ltering of noisy images.