期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 65, 期 17, 页码 4481-4494出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2017.2711501
关键词
Sparse regularization; sparse approximation; convex function; optimization; denoising
资金
- National Science Foundation [CCF-1525398]
- ONR [N00014-15-1-2314]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1525398] Funding Source: National Science Foundation
Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of nonconvex penalty functions that maintain the convexity of the least squares cost function to be minimized, and avoids the systematic underestimation characteristic of L1 norm regularization. The proposed penalty function is a multivariate generalization of the minimax-concave penalty. It is defined in terms of a new multivariate generalization of the Huber function, which in turn is defined via infimal convolution. The proposed sparse-regularized least squares cost function can be minimized by proximal algorithms comprising simple computations.
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