A class of singular diffusion equations based on the convex–nonconvex variation model for noise removal

This paper focuses on the problem of noise removal. First, we propose a new convex–nonconvex variation model for noise removal and consider the nonexistence of solutions of the variation model. Based on the new variation method, we propose a class of singular diffusion equations and prove the of solutions and comparison rule for the new equations. Finally, experimental results illustrate the effectiveness of the model in noise reduction.