HAF: An adaptive fuzzy filter for restoring highly corrupted images by histogram estimation

Abstract

This paper presents a novel adaptive approach to image restoration using fuzzy spatial filtering optimized via image statistics rather than a prior knowledge of specific image data. The proposed histogram adaptive fuzzy (HAF) filter is particularly effective for removing highly impulsive noise while preserving edge sharpness. This is accomplished through a fuzzy smoothing filter constructed from a set of fuzzy IF-THEN rules, which alternate adaptively to minimize the output mean squared error as input histogram statistics change. An algorithm is developed to utilize (corrupted) input histogram to determine parameters for the near- optimal fuzzy membership functions. Construction of the HAF filter involves three steps: (1) define fuzzy sets in the input space, (2) construct a set of IF-THEN rules by incorporating input histogram statistics to form the fuzzy membership functions, and (3) construct the filter based on the set of rules. Similar to the conventional median filters (MF), the proposed method has the following merits: it is simple, and it assumes no a priori knowledge of a specific input image, yet it has superior performance compared to other existing ranked-order filters (including MF) for the full range of impulsive noise probability. Unlike many neuro-fuzzy or fuzzy-neuro filters, where a random strategy is employed to choose initial membership functions for subsequent lengthy training, HAF can achieve near-optimal performance without any training.