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.

中文翻译：

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一种有效的彩色图像复原乘法器交替方向法

摘要 彩色图像恢复是一个不适定问题，需要进行正则化。在本文中，我们首先将彩色图像恢复问题表述为一个约束最小化问题，该问题最小化二次函数，并受到彩色图像总变化小于给定参数 δ 的约束。约束最小化问题相对于传统无约束最小化问题的优势在于参数δ具有明显的物理意义且易于选择。然而，解决约束最小化问题通常比解决相应的无约束形式更困难。我们利用问题的结构提出了一种有效的乘法器交替方向方法用于彩色图像恢复。我们详细证明了该方法的收敛性。