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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
2019 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 155, p. 247-258Article in journal (Refereed) Published
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
Elsevier, 2019. Vol. 155, p. 247-258
Keywords [en]
Compressive sensing, q-ratio sparsity, q-ratio constrained minimal singular values, Convex–concave procedure
National Category
Signal Processing Probability Theory and Statistics
Research subject
Mathematical Statistics; Signal Processing
Identifiers
URN: urn:nbn:se:umu:diva-152530DOI: 10.1016/j.sigpro.2018.10.002ISI: 000452585600019Scopus ID: 2-s2.0-85054424540OAI: oai:DiVA.org:umu-152530DiVA, id: diva2:1254716
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-534Available from: 2018-10-10 Created: 2018-10-10 Last updated: 2019-02-28Bibliographically approved

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Zhou, ZhiyongYu, Jun

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