Signal recovery by proximal forward-backward splitting
Signal recovery by proximal forward-backward splitting
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DOI：
10.1137/050626090
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发表时间：
2005-01-01
影响因子：
1.6
通讯作者：
Wajs, VR
中科院分区：
文献类型：
--
作者：
Combettes, PL;Wajs, VR
我们表明，信号恢复中的各种逆问题可以制定为具有一定的规律性的两个凸函数的和最小化的一般问题。这种提法使得有可能获得存在性，唯一性，特征，和稳定性的结果，在一个统一的和标准化的方式为一大类明显不同的问题。最近的单调算子分裂方法的结果，建立一个向前向后算法来解决一般问题的收敛性。反过来，我们恢复，扩展，并提供了一个简化的分析各种现有的迭代方法。几何/纹理图像分解方案的应用进行了讨论。我们的框架的一个新奇是广泛使用的邻近算子，这是由莫罗在20世纪60年代推出的概念。
We show that various inverse problems in signal recovery can be formulated as the generic problem of minimizing the sum of two convex functions with certain regularity properties. This formulation makes it possible to derive existence, uniqueness, characterization, and stability results in a unified and standardized fashion for a large class of apparently disparate problems. Recent results on monotone operator splitting methods are applied to establish the convergence of a forward-backward algorithm to solve the generic problem. In turn, we recover, extend, and provide a simplified analysis for a variety of existing iterative methods. Applications to geometry/texture image decomposition schemes are also discussed. A novelty of our framework is to use extensively the notion of a proximity operator, which was introduced by Moreau in the 1960s.