Remove the salt and pepper noise based on the high order total variation and the nuclear norm regularization

This paper proposes a new model to remove the salt and pepper (SAP) noise problem. In the proposed method, we combine the high order total variation regularization with the nuclear norm regularization in order to keep details and structures of the restored images. Since the proposed model is convex and separable, the classic alternating direction method of multipliers can be employed to solve it by introducing some auxiliary variables to transform the original problem into the saddle point problem. Theoretically, we establish the convergence analysis of the proposed numerical algorithm. Final experimental comparisons are provided to show the satisfactory performance of the proposed model, which outperforms other related competitive methods in both the SNR and the SSIM. (C) 2022 Published by Elsevier Inc.

Automated summary

This paper proposes a new model for removing salt and pepper noise by combining high order total variation regularization with nuclear norm regularization. The model is convex and separable, and the classic alternating direction method of multipliers is used to solve it. The experimental comparisons demonstrate that the proposed model outperforms other methods in terms of signal-to-noise ratio (SNR) and structural similarity index (SSIM).