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Sparse recovery based on q-ratio constrained minimal singular values
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620X
2018 (English)Manuscript (preprint) (Other academic)
Abstract [en]

We study verifiable sufficient conditions and computable performance bounds for sparse recovery algorithms such as the Basis Pursuit, the Dantzig selector and the Lasso estimator, in terms of a newly defined family of quality measures for the measurement matrices. With high probability, the developed measures for subgaussian random matrices are bounded away from zero as long as the number of measurements is reasonably large. Comparing to the restricted isotropic constant based performance analysis, the arguments in this paper are much more concise and the obtained bounds are tighter. Numerical experiments are presented to illustrate our theoretical results.

Place, publisher, year, edition, pages
2018. , p. 26
Keywords [en]
Compressive sensing; q-ratio sparsity; q-ratio constrained minimal singular values; Convex-concave procedure.
National Category
Probability Theory and Statistics Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-144131OAI: oai:DiVA.org:umu-144131DiVA, id: diva2:1176286
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-534Available from: 2018-01-22 Created: 2018-01-22 Last updated: 2018-06-09

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arxiv: 1801.06358

Authority records BETA

Zhou, ZhiyongYu, Jun

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CiteExportLink to record
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