Fast Algorithms for Weighted Myriad Computation by Fixed Point Search

This paper addresses the problem of computation of the output of the Weighted Myriad Filter. Weighted Myriad Filters form a large and important class of nonlinear filters that includes linear FIR filters, with several potential applications in robust signal processing and communications in impulsive non-Gaussian environments. Just as the weighted mean and the weighted median are optimized for the Gaussian and Laplacian distributions, respectively, the weighted myriad is derived based on the properties of ff-stable distributions, which have been shown to accurately model practically occurring impulsive processes. The weighted myriad is an M-estimator that is defined in an implicit manner; no closed-form expression exists for its computation, and its direct computation is a non-trivial and prohibitively expensive task. In this paper, the weighted myriad is formulated as one of the fixed points of a certain mapping. An iterative algorithm is proposed to compute these fixed points, and it..