21 Order-statistic filtering and smoothing of time-series: Part II

Publisher Summary This chapter discusses the fundamentals of weighted order-statistic filters and permutation weighted order-statistic filters. The simplest of these, the median and center weighted median (CWM) filters, are described through their statistical and deterministic properties. Filters can be designed by varying the center weight of CWM filters. For the larger class of weighted median and permutation weighted order statistic filters, the chapter presents a design methodology based on the minimization of the mean absolute error (MAE) of the estimate. These methods rely on the threshold decomposition property characteristic of these filters. Two simple adaptive filter algorithms are presented in the chapter, which can be used to train permutation weighted order statistic (WOS) filters. Thus, given a desired signal and a corresponding observation sequence, a permutation weighted order-statistic (PWOS) filter can be easily design for any application where the training signals can be made available To illustrate the performance of WOS and PWOS filters, the chapter reviews the image restoration problem, where a video sequence is corrupted by impulsive noise and a tone interference. Using the adaptive algorithms, the video sequence using several PWOS filters are restored and are compared in the chapter with the L j l type filters. It shows that PWOS filters preserve edges and discontinuities more effectively than Ug filters; however, L j l filters have more flexibility because their output is not constrained by the input value set. The applications presented in the chapter are biased toward digital image and video communications. WOS and PWOS filters, however, can be readily used in other applications of time series analysis.