Parameter Selection for Total-Variation-Based Image Restoration Using Discrepancy Principle
Parameter Selection for Total-Variation-Based Image Restoration Using Discrepancy Principle
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DOI：
10.1109/tip.2011.2181401
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发表时间：
2012-04-01
影响因子：
10.6
通讯作者：
Chan, Raymond H.
中科院分区：
文献类型：
--
作者：
Wen, You-Wei;Chan, Raymond H.
成功解决图像恢复问题有两个关键问题：1）平衡数据保真度与解的正则性的正则化参数的估计; 2）开发用于计算解的有效数值技术。在本文中，我们推导出一个快速算法，同时估计正则化参数和恢复图像。新方法是基于全变分（TV）正则化策略和Morozov的差异原则。TV范数由对偶公式表示，该对偶公式将最小化问题变为极大极小化问题。提出了一种计算极大极小问题鞍点的近似点方法。通过在每次迭代中自适应地调整正则化参数，保证解满足偏差原理。我们将给出我们的算法的收敛性证明，并数值表明，它是优于一些国家的最先进的方法在速度和精度方面。
There are two key issues in successfully solving the image restoration problem: 1) estimation of the regularization parameter that balances data fidelity with the regularity of the solution and 2) development of efficient numerical techniques for computing the solution. In this paper, we derive a fast algorithm that simultaneously estimates the regularization parameter and restores the image. The new approach is based on the total-variation (TV) regularized strategy and Morozov's discrepancy principle. The TV norm is represented by the dual formulation that changes the minimization problem into a minimax problem. A proximal point method is developed to compute the saddle point of the minimax problem. By adjusting the regularization parameter adaptively in each iteration, the solution is guaranteed to satisfy the discrepancy principle. We will give the convergence proof of our algorithm and numerically show that it is better than some state-of-the-art methods in terms of both speed and accuracy.