Cauchy Noise Removal via Convergent Plug-and-Play Framework with Outliers Detection

Restoring natural images corrupted by Cauchy noise is a challenging issue in image processing. In the existing methods, the traditional model-driven and filter-based methods can not recover the images well, and the learning-based plug-and-play method lacks convergence guarantees. In this paper, we propose a convergent plug-and-play method with outliers detection (C-PnPO) to remove Cauchy noise. The outlier detection is based on an outlier map regularized by maximum entropy. Due to the statistical properties of Cauchy distribution and the implicit deep image priors, the problem is non-convex and implicit. We present a convergent algorithm to address these issues by an adaptively relaxed alternating direction method of multipliers. Theoretically, we give some useful mathematical properties, including the existence of solutions under mild assumptions, and the global linear convergence of the proposed method by an adaptive relaxation strategy. Experimental results show that the outliers can be successfully detected, and the proposed method outperforms the existing state-of-art traditional and learning-based methods both in terms of quantitative and qualitative comparisons.