Signal-dependent rank-ordered-mean (SD-ROM) filter

TLDR: This chapter presents the signal-dependent rank-ordering-mean (SD-ROM) method for the removal of impulse noise from image data, in which the filtering operation is conditioned on the rank-ordered differences, defined as the differences between the input pixel and the remaining rank- ordered pixels in a sliding window.

Abstract: Publisher Summary This chapter presents the signal-dependent rank-ordered-mean (SD-ROM) method for the removal of impulse noise from image data, in which the filtering operation is conditioned on the rank-ordered differences, defined as the differences between the input pixel and the remaining rank-ordered pixels in a sliding window. The chapter discusses two algorithms—one based on a simple detection-estimation strategy involving thresholds, and the other incorporating fuzzy rules. The strategies for the design of the weighting coefficients are presented in the algorithm incorporating fuzzy rules, for recursive and non-recursive implementation, including a least-squares derivation for the non-recursive case, which leads to a close form expression for the optimal weighting coefficients. This chapter also presents computer simulation examples to illustrate the effectiveness of the SD-ROM method using several distinct noise types, including impulsive, Gaussian, and mixed impulsive and Gaussian. Finally, it presents a simple algorithm for restoration of images corrupted by streaks, based on the SD-ROM approach.