An effective alternating direction method of multipliers for color image restoration

Color image restoration is an ill-posed problem, and regularization is necessary. In this paper, we first formulate the color image restoration problem into a constrained minimization problem that minimizes a quadratic functional and subject to a constraint that the total variation of the color image is less than a given parameter delta. The advantages of the constrained minimization problem over the traditional unconstrained one is that the parameter delta has an obvious physical meaning and is easy to select. However solving the constrained minimization problem is generally more difficult than solving the corresponding unconstrained form. We propose an effective alternating direction method of multipliers for color image restoration by using the structure of the problem. We prove the convergence of the method in detail. Experimental results demonstrate that the proposed method is feasible and much more effective for color image restoration. (c) 2020 IMACS. Published by Elsevier B.V. All rights reserved.

Automated summary

This study focuses on color image restoration as an ill-posed problem that requires regularization. By formulating the problem as a constrained minimization problem and proposing an effective alternating direction method of multipliers, the paper demonstrates that the proposed method is feasible and much more effective for color image restoration.