Image restoration based on the minimized surface regularization

We propose an image restoration model based on the minimized surface regularization. The proposed model closely relates to the classical smoothing ROF model (Rudin et al., 1992). We deduce two different conjugation forms via coupling the gradient operator with the smoothing parameter α or not, and then provide the existence of the minimizer in the continuous setting. In order to efficiently solving the proposed model, we employ the primal dual method by reformulating the proposed model as a min-max problem. Relying on the convex conjugation, the convergence of the algorithm is provided as well. Numerical implementations mainly emphasize the effectiveness of the proposed method by comparing it to other two well-known methods in terms of the CPU time and restoration quality.