Introduction

Abstract

In the early development of signal and image processing, linear filters were the primary tools. Their mathematical simplicity and the existence of some desirable properties made them easy to design and implement. Moreover, linear filters offered satisfactory performance in many applications. However, linear filters have poor performance in the presence of noise that is not additive as well as in problems where system nonlinearities or non-Gaussian statistics are encountered. In addition, various criteria, such as the maximum entropy criterion, lead to nonlinear solutions. In image processing applications, linear filters tend to blur the edges, do not remove impulsive noise effectively, and do not perform well in the presence of signal dependent noise. It is also known that, although the exact characteristics of our visual system are not well understood, experimental results indicate that the first processing levels of our visual system possess nonlinear characteristics. For such reasons, nonlinear filtering techniques for signal/image processing were considered as early as 1958 [1].