Fast algorithms for weighted myriad computation by fixed-point search

This paper develops fast algorithms to compute the output of the weighted m yriad filter. Myriad filters form a large and important class of nonlinear filters for robust non-Gaussian signal processing and communications in imp ulsive noise environments. Just as the weighted mean and the weighted media n are optimized for the Gaussian and Laplacian distributions, respectively, the weighted myriad is based on the class of alpha-stable distributions, w hich can accurately model impulsive processes. The weighted myriad is an M-estimator that is defined in an implicit manner ; no closed-form expression exists for it, and its direct computation is a nontrivial and prohibitively expensive task, In this paper, the weighted my riad is formulated as one of the fixed points of a certain mapping. An iter ative algorithm is proposed to compute these fixed points, and its converge nce is proved rigorously, Using these fixed-point iterations, fast algorith ms are developed for the weighted myriad, Numerical simulations demonstrate that these algorithms compute the weighted myriad with a high degree of ac curacy at a relatively low computational cost.