Image Denoising using Alexander Fractional Hybrid Filter

Abstract

In this paper, a hybrid filter based on the concept of fractional calculus and Alexander polynomial is proposed. The hybrid filtering mask is constructed by convolving the designed Alexander fractional differential and integral masks. The hybrid mask shows high robustness for images corrupted with Gaussian, salt & pepper, and speckle noises. For the experimentation, the standard and real world noisy images are used. The qualitative comparison shows that the proposed hybrid filter has better denoising with high edge preserving capability as compared to the other existing filters. Quantitatively, the performance of the proposed hybrid filter is also evaluated by the measures such as peak signal to noise ratio (PSNR), normalized cross-correlation (NK), average difference (AD), structural content (SC), maximum difference (MD) and normalized absolute error (NAE) on standard set of images. The average values of these metrics for Gaussian noise with maximum standard deviation [Formula: see text] are PSNR [Formula: see text] 32.729, NK [Formula: see text] 0.8190, AD [Formula: see text] 0.01825, SC [Formula: see text] 0.8527, MD [Formula: see text] 87, NAE [Formula: see text] 0.0637. The experimentation reveals that the proposed hybrid filter gives better improvement as compared with other existing filters both qualitatively and quantitatively.