An Image-Denoising Framework Using ℓq Norm-Based Higher Order Variation and Fractional Variation with Overlapping Group Sparsity

As one of the most significant issues in imaging science, image denoising plays a major role in plenty of image processing applications. Due to the ill-posed nature of image denoising, total variation regularization is widely used in image denoising problems for its capability to suppress noise and preserve image edges. Nevertheless, traditional total variation will inevitably yield undesirable staircase artifacts when applied to recorded images. Inspired by the success of ℓq norm minimization and overlapping group sparsity in image denoising, and the effective staircase artifacts removal by fractional total variation, the hybrid model which combines the fractional order total variation with overlapping group sparsity and higher order total variation with ℓq norm is developed in this paper to restore images corrupted by Gaussian noise. An efficient algorithm based on the parallel linear alternating direction method of multipliers is developed for solving the corresponding model and the numerical experiments demonstrate the effectiveness of the proposed approach against several state-of-the-art methods, in terms of peak signal-to-noise ratio and structure similarity index measure values.