Lp norm design of weighted order statistic filters

This paper addresses the problem of designing weighted order statistic (WOS) filters by employing an objective function given as the L_p norm of the error between the desired signal and the estimated one. The conventional design of WOS filters uses a mean absolute error (MAE) objective function, and as such, it is a special case of the general, L_p norm based design, developed here. It is shown that in stack filtering, the L_p norm can be expressed as a linear combination of the decision errors incurred by the Boolean operators at each level of the stack filter architecture. Based on this formulation of the L_p norm, both nonadaptive and adaptive algorithms for the design of L_p WOS filters are developed. A design example is considered, to illustrate the performance of the designed L_p WOS filters with different values of p. The simulation results show that the L_p WOS filters with p⩾2 are capable of removing more impulsive noise compared with the conventional MAE WOS filters