Convex Image Denoising via Non-Convex Regularization

Natural image statistics motivate the use of non-convex over convex regularizations for restoring images. However, they are rarely used in practice due to the challenge to find a good minimizer. We propose a Convex Non-Convex (CNC) denoising variational model and an efficient minimization algorithm based on the Alternating Directions Methods of Multipliers (ADMM) approach. We provide theoretical convexity conditions for both the CNC model and the optimization sub-problems arising in the ADMM-based procedure, such that convergence to a unique global minimizer is guaranteed. Numerical examples show that the proposed approach is particularly effective and well suited for images characterized by sparse-gradient distributions.