  Models including two $L^1$ -norm terms have been widely used in image
restoration. In this paper we first propose the alternating direction method of
multipliers (ADMM) to solve this class of models. Based on ADMM, we then
propose the proximal point method (PPM), which is more efficient than ADMM.
Following the operator theory, we also give the convergence analysis of the
proposed methods. Furthermore, we use the proposed methods to solve a class of
hybrid models combining the ROF model with the LLT model. Some numerical
results demonstrate the viability and efficiency of the proposed methods.
