A relaxed Newton–Picard like method for Huber variant of total variation based image restoration

Abstract

In this paper, we propose an effective iteration method for Huber variant of total variation based image restoration by exploiting the structure of the problem. We call the proposed method relaxed Newton–Picard like method. This method is easy to implement and cost-effective. We prove the convergence of the method by using the theory on semismooth functions. Experimental results show that the proposed method is more efficient than the alternating minimization method based on multiplicative half-quadratic reformulation and is competitive with the state of the art alternating direction method of multipliers.