An effective alternating direction method of multipliers for color image restoration

Abstract 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 δ. The advantages of the constrained minimization problem over the traditional unconstrained one is that the parameter δ 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.