Fast Image Recovery Using Variable Splitting and Constrained Optimization
Fast Image Recovery Using Variable Splitting and Constrained Optimization
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DOI：
10.1109/tip.2010.2047910
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发表时间：
2010-09-01
影响因子：
10.6
通讯作者：
Figueiredo, Mario A. T.
中科院分区：
文献类型：
--
作者：
Afonso, Manya V.;Bioucas-Dias, Jose M.;Figueiredo, Mario A. T.
我们提出了一种新的快速算法来解决图像恢复和重建的标准公式之一，其中包括一个无约束的优化问题，目标包括一个数据保真度项和一个非光滑正则化。该公式允许基于小波（具有正交或基于帧的表示）的正则化或全变差正则化。我们的方法是基于变量分裂，以获得一个等价的约束优化配方，然后与增广拉格朗日方法。所提出的算法是所谓的交替方向的乘法器，收敛性已被证明的方法的一个实例。一组图像恢复和重建基准问题的实验表明，该算法比目前的最先进的方法是快速的。
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods.