Least Mean Fourth Based Constrained Adaptive Order Statistic Filters For Image Restoration

Abstract

This paper proposes the adaptive constrained order statistic L and combination C (Ll) filter using the least mean fourth algorithm (LMF) with linear and non-linear structures at the output. Though, the LMF problem involves many stability problems due to noise variance and increase of input power. This can be avoided in Normalized Least Mean Fourth (NLMF) algorithm by normalising the weight update terms by the fourth power norm of the regressor. Here the LMF based adaptive L filter is derived with linear and non linear output of a fixed window. Whereas the adaptive C filter uses the rank order and temporal order information from the input sequence of fixed window. These filters use ordered data to remove non-Gaussian noise components, preserves the edges and details of an image. In this paper, the performance of C filter overrides the performance of the LMF-L and other LMF based filters.