A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

Abstract

Denoising images subjected to Gaussian and Poisson noise has attracted attention in many areas of image processing. This paper introduces an image denoising framework using higher order fractional overlapping group sparsity prior to sparser image representation constraint. The proposed prior has a capability of avoiding staircase effects in both edges and oscillatory patterns (textures). We adopt the alternating direction method of multipliers for optimizing the proposed objective function by converting it into a constrained optimization problem using variable splitting approach. Finally, we conduct experiments on various degraded images and compare our results with those of several state-of-the-art methods. The numerical results show that the proposed fractional order image denoising framework improves the peak signal to noise ratio of an image by preserving the textures and eliminating the staircases effects. This leads to visually pleasant restored images which exhibit a higher value of Structural SIMilarity score when compared to that of other methods. INDEX TERMS Image denoising, fractional-order, Gaussian and Poisson noise, overlapping group sparsity, alternating direction method of multipliers.

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