Bayesian Selective Median Filtering for Reduction of Impulse Noise in Digital Color Images

Abstract

The focus of this paper is impulse noise reduction in digital color images. The most popular noise reduction schemes are the vector median filter and its many variants that operate by minimizing the aggregate distance from one pixel to every other pixel in a chosen window. This minimizing operation determines the most confirmative pixel based on its similarity to the chosen window and replaces the central pixel of the window with the determined one. The peer group filters, unlike the vector median filters, determine a set of pixels that are most confirmative to the window and then perform filtering over the determined set. Using a set of pixels in the filtering process rather than one pixel is more helpful as it takes into account the full information of all the pixels that seemingly contribute to the signal. Hence, the peer group filters are found to be more robust to noise. However, the peer group for each pixel is computed deterministically using thresholding schemes. A wrong choice of the threshold will easily impair the filtering performance. In this paper, we propose a peer group filtering approach using principles of Bayesian probability theory and clustering. Here, we present a method to compute the probability that a pixel value is clean (not corrupted by impulse noise) and then apply clustering on the probability measure to determine the peer group. The key benefit of this proposal is that the need for thresholding in peer group filtering is completely avoided. Simulation results show that the proposed method performs better than the conventional vector median and peer group filtering methods in terms of noise reduction and structural similarity, thus validating the proposed approach.