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Enhanced block sparse signal recovery based on q-ratio block constrained minimal singular values
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Department of Statistics, Zhejiang University City College, Hangzhou, China.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620X
2019 (English)Manuscript (preprint) (Other academic)
Abstract [en]

In this paper we introduce theq-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ2/ℓq and the mixed ℓ2/ℓ1 norms of the reconstruction errors for stable and robust recovery using block Basis Pursuit (BBP), the block Dantzig selector (BDS) and the group lasso in terms of the q-ratio BCMSV are investigated. We establish a sufficient condition based on the q-ratio block sparsity for the exact recovery from the noise free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, theq-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the q-ratio BCMSV based error bounds are tighter than the block restricted isotropic constant based bounds.

Place, publisher, year, edition, pages
2019. , p. 20
Keywords [en]
Compressive sensing;q-ratio block sparsity;q-ratio block constrained minimal singularvalue; Convex-concave procedure
National Category
Signal Processing Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-162953OAI: oai:DiVA.org:umu-162953DiVA, id: diva2:1348154
Part of project
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment, Swedish Research CouncilAvailable from: 2019-09-03 Created: 2019-09-03 Last updated: 2019-09-04

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arXiv August 2019

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CiteExportLink to record
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Citation style
  • apa
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  • asciidoc
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