期刊
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
卷 14, 期 5-6, 页码 764-792出版社
SPRINGER BIRKHAUSER
DOI: 10.1007/s00041-008-9039-8
关键词
Linear inverse problems; Sparse recovery; Projected gradient method
资金
- European Union's Human Potential Programme [MOIF-CT-2006-039438]
- NSF [DMS-0245566, 0530865]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0530865] Funding Source: National Science Foundation
Regularization of ill-posed linear inverse problems via l(1) penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an l(1) penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to l(1)-constraints, using a gradient method, with projection on l(1)-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence
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