Adaptive algorithms for Weighted Myriad Filter optimization

Stochastic gradient-based adaptive algorithms are developed for the optimization of weighted myriad filters, a class of nonlinear filters, motivated by the properties of α-stable distributions, that have been proposed for robust non-Gaussian signal processing in impulsive noise environments. An implicit formulation of the filter output is used to derive an expression for the gradient of the mean absolute error (MAE) cost function, leading to necessary conditions for the optimal filter weights. An adaptive steepest-descent algorithm is then derived to optimize the filter weights. This is modified to yield an algorithm with a very simple weight update, computationally comparable to the update in the classical LMS algorithm. Simulations demonstrate the robust performance of these algorithms