An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
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DOI：
10.1002/cpa.20042
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发表时间：
2004-11-01
影响因子：
3
通讯作者：
De Mol, C
中科院分区：
文献类型：
--
作者：
Daubechies, I;Defrise, M;De Mol, C
我们考虑线性反问题的解决方案被假定为有一个稀疏的扩展在一个任意的预分配的正交基础。我们证明，用此类展开式系数的加权l（p）-罚分（其中1小于或等于p小于或等于2）替换通常的二次正则化罚分，仍然可以正则化问题。当人们期望潜在的理想无噪声解相对于所考虑的基具有稀疏展开时，通常提倡使用p < 2的l（p）-惩罚问题。为了计算相应的正则化的解决方案，我们分析了一个迭代算法，相当于一个Landweber迭代与阈值（或非线性收缩）应用在每个迭代步骤。我们证明了该算法在范数下收敛。(C)2004 Wiley Periodicals，Inc.
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l(p)- penalties on the coefficients of such expansions, with 1 less than or equal to p less than or equal to 2, still regularizes the problem. Use of such l(p)-penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under consideration. To compute the corresponding regularized solutions, we analyze an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. (C) 2004 Wiley Periodicals, Inc.