1 - Analysis and Optimization of Weighted Order Statistic and Stack Filters

Abstract

This chapter discusses stack and weighted order statistic filters and describes the tools available for their analysis and optimization. The median filter was introduced for smoothing of discrete data. Median filters attenuate impulsive noise effectively and preserve signal edges well. Therefore, they are used in signal processing. The median filter has a weighted version, the order statistic filter. The order statistic filter also has a weighted version, called the weighted order statistic (WOS) filter. The stack filter shares two important properties of the median filter—threshold decomposition and stacking properties. This chapter examines the main deterministic properties of these filters including impulse and step responses as well as root signals. It also investigates the statistical properties by using output distributions and moments. In addition, it defines the concepts of selection probability, finite-sample breakdown point, breakdown probability, and output distributional influence function and introduces their basic properties as possible tools for analyzing and optimizing these filters. Finally, the chapter presents some optimization examples and discusses the application of these filters to image processing.