Saturation-value based higher-order regularization for color image restoration

In this article, we introduce saturation-value based higher-order (SV-HO) regularizers and propose several color image restoration models using these regularizers. The SV-HO regularization not only ameliorates the staircasing artifacts caused by the total variation based regularization, but it also significantly reduces the artificial colors induced by the RGB based regularization. Furthermore, incorporating SV-HO with nonconvexity contributes the conservation of edges in the restored images. The effects of convex or nonconvex SV-HO are demonstrated in some color image restoration problems, such as denoising and/or deblurring under Gaussian noise and denoising under multiplicative noise. To resolve the proposed nonconvex models, we adopt an iteratively reweighted L1 algorithm and an alternating direction method of multipliers. These procedures lead to efficient iterative algorithms, and their convergence is proven. The experimental results validate that the SV-HO based models outperform the existing or related models in terms of visual aspect and image quality assessments.