Image Restoration Based on the Hybrid Total-Variation-Type Model

Abstract

We propose a hybrid total-variation-type model for the image restoration problem based on combining advantages of the ROF model with the LLT model. Since two $L^1$-norm terms in the proposed model make it difficultly solved by using some classically numerical methods directly, we first employ the alternating direction method of multipliers (ADMM) to solve a general form of the proposed model. Then, based on the ADMM and the Moreau-Yosida decomposition theory, a more efficient method called the proximal point method (PPM) is proposed and the convergence of the proposed method is proved. Some numerical results demonstrate the viability and efficiency of the proposed model and methods.