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On q-ratio CMSV for sparse recovery
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. 165, p. 128-132Article in journal (Refereed) Published
Abstract [en]

As a kind of computable incoherence measure of the measurement matrix, q-ratio constrained minimal singular values (CMSV) was proposed in Zhou and Yu (2019) to derive the performance bounds for sparse recovery. In this paper, we study the geometrical properties of the q-ratio CMSV, based on which we establish new sufficient conditions for signal recovery involving both sparsity defect and measurement error. The ℓ1-truncated set q-width of the measurement matrix is developed as the geometrical characterization of q-ratio CMSV. In addition, we show that the q-ratio CMSVs of a class of structured random matrices are bounded away from zero with high probability as long as the number of measurements is large enough, therefore these structured random matrices satisfy those established sufficient conditions. Overall, our results generalize the results in Zhang and Cheng (2012) from q=2 to any q ∈ (1, ∞] and complement the arguments of q-ratio CMSV from a geometrical view.

Place, publisher, year, edition, pages
Elsevier, 2019. Vol. 165, p. 128-132
Keywords [en]
Sparse recovery, q-ratio sparsity, q-ratio constrained minimal singular values, ℓ1-truncated set q-width
National Category
Signal Processing Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-161379DOI: 10.1016/j.sigpro.2019.07.003OAI: oai:DiVA.org:umu-161379DiVA, id: diva2:1334627
Part of project
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment, Swedish Research Council
Funder
Swedish Research Council, 340-2013-5342Available from: 2019-07-03 Created: 2019-07-03 Last updated: 2019-07-15

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Zhou, ZhiyongYu, Jun

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CiteExportLink to record
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