Lp norm design of weighted order statistic filters

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