20 Order-statistic filtering and smoothing of time-series: Part I

Abstract

This chapter discusses the concept of order-statistic filtering and smoothing of time-series. It illustrates that nonlinear filters can outperform linear methods in applications where the underlying random processes are non-Gaussian or when system nonlinearities are present. Nonlinear and non-Gaussian processes are quite common in signal processing applications. Examples of waveforms include sea clutter in radar, speech waveforms, image and video signals, and many digital communication signals. Image and video signals contain edges, details, scenes, and colors that can abruptly change from one sample to another. If linear filters are used to estimate these signals from their corresponding noisy observations, the resulting linear estimates will unavoidably yield blurred signals that, in many cases, are objectionable to the end user. Linear filters fail to preserve those fine features that are of great importance to visual perception. These facts agree with statistical principles, which dictate that nonlinear estimation is advantageous for time series that are non-Gaussian in nature. While second-order moments are sufficient to effectively process Gaussian processes, more powerful statistics must be exploited for the processing of non-Gaussian or nonlinear time series.