A proximal decomposition method for solving convex variational inverse problems
A proximal decomposition method for solving convex variational inverse problems
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DOI：
10.1088/0266-5611/24/6/065014
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发表时间：
2008-12-01
期刊：
影响因子：
2.1
通讯作者：
Pesquet, Jean-Christophe
中科院分区：
文献类型：
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作者：
Combettes, Patrick L.;Pesquet, Jean-Christophe
一系列的反问题可以抽象为希尔伯特空间中几个凸函数之和的最小化问题。我们提出了一个近似分解算法来解决这一问题，并证明了它的弱收敛性质。该算法完全分解了问题，因为它通过每个函数各自的邻近性算子分别涉及到每个函数。与目前在反问题领域中使用的方法相比，一个显著的改进是它不限于两个非光滑函数。给出了信号和图像处理问题的数值应用。
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of nonsmooth functions and establish its weak convergence. The algorithm fully decomposes the problem in that it involves each function individually via its own proximity operator. A significant improvement over the methods currently in use in the area of inverse problems is that it is not limited to two nonsmooth functions. Numerical applications to signal and image processing problems are demonstrated.