Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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. 57Article in journal (Refereed) Epub ahead of print
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. 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/s13634-019-0653-1OAI: 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 CouncilAvailable from: 2019-12-02 Created: 2019-12-02 Last updated: 2019-12-03

Open Access in DiVA

fulltext(1452 kB)6 downloads
File information
File name FULLTEXT01.pdfFile size 1452 kBChecksum SHA-512
deef839f8287a1239f081bbfa8c9eb94a5e89866227d67d9f633e71baea7a67b610aea2f3d3be3f92d1a2b26fa69ea2ee3c9f0d1bd8d15c472d2b04984fca14f
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Wang, JianfengYu, Jun
By organisation
Department of Mathematics and Mathematical Statistics
In the same journal
EURASIP Journal on Advances in Signal Processing
Signal ProcessingProbability Theory and StatisticsComputational Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 6 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 6 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf