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Error bounds of 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, China.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620x
2019 (English)In: EURASIP Journal on Advances in Signal Processing, ISSN 1687-6172, E-ISSN 1687-6180, Vol. 2019, article id 57Article in journal (Refereed) Published
Abstract [en]

In this paper, we introduce the q-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, the q-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
Springer, 2019. Vol. 2019, article id 57
Keywords [en]
Compressive sensing, q-ratio block sparsity, q-ratio block constrained minimal singular value, Convex-concave procedure
National Category
Signal Processing Probability Theory and Statistics Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-165632DOI: 10.1186/s13634-019-0653-1ISI: 000499457500002OAI: oai:DiVA.org:umu-165632DiVA, id: diva2:1374655
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: 2019-12-02 Created: 2019-12-02 Last updated: 2020-01-09Bibliographically approved

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Wang, JianfengYu, Jun

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