MRL-FILTERS - A GENERAL-CLASS OF NONLINEAR-SYSTEMS AND THEIR OPTIMAL-DESIGN FOR IMAGE-PROCESSING

In this paper, the class of morphological/rank/linear (MRL)-filters is presented as a general nonlinear tool for image processing. They cons ist of a linear combination between a morphological/rank filter and a linear filter. A gradient steepest descent method is proposed to optim ally design these filters, using the averaged least mean squares (LMS) algorithm. The filter design is viewed as a learning process, and con vergence issues are theoretically and experimentally investigated. A s ystematic approach is proposed to overcome the problem of nondifferent iability of the nonlinear filter component and to improve the numerica l robustness of the training algorithm, which results in simple traini ng equations. Image processing applications in system identification a nd image restoration are also presented, illustrating the simplicity o f training MRL-filters and their effectiveness for image/signal proces sing.