A class of null space conditions for sparse recovery via nonconvex, non-separable minimizations

For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than ℓ₁ penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) ℓ₁ minimization in exact, uniform recovery...

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Bibliographic Details
Published inResults in applied mathematics Vol. 3; no. C; p. 100011
Main Authors Tran, Hoang, Webster, Clayton
Format Journal Article
LanguageEnglish
Published Netherlands Elsevier 01.10.2019
Subjects
Majorization theory
MATHEMATICS AND COMPUTING
Nonconvex optimization
Null space property
Sparse recovery
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ISSN2590-0374
2590-0374
DOI10.1016/j.rinam.2019.100011

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Summary:For the problem of sparse recovery, it is widely accepted that nonconvex minimizations are better than ℓ₁ penalty in enhancing the sparsity of solution. However, to date, the theory verifying that nonconvex penalties outperform (or are at least as good as) ℓ₁ minimization in exact, uniform recovery has mostly been limited to separable cases. In this paper, we establish general recovery guarantees through null space conditions for nonconvex, non-separable regularizations, which are slightly less demanding than the standard null space property for ℓ₁ minimization.
Bibliography:USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
ERKJ314; ERKJ331; ERKJ345; AC02-05CH11231; AC05-00OR22725
ISSN:2590-0374
2590-0374
DOI:10.1016/j.rinam.2019.100011