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Sparsity estimation in compressive sensing with application to MR images
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.
Umeå University, Faculty of Medicine, Department of Radiation Sciences.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (Mathematical Statistics)ORCID iD: 0000-0001-5673-620X
2017 (English)Manuscript (preprint) (Other academic)
Abstract [en]

The theory of compressive sensing (CS) asserts that an unknown signal x in C^N canbe accurately recovered from m measurements with m << N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||_0 as an input. However,generally s is unknown, and directly estimating the sparsity has been an open problem.In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. Inthe simulation study and real data study, magnetic resonance image data is used asinput signal, which becomes sparse after sparsified transformation. The results fromthe simulation study confirm the theoretical properties of the estimator. In practice, theestimate from a real MR image can be used for recovering future MR images under theframework of CS if they are believed to have the same sparsity level after sparsification.

Place, publisher, year, edition, pages
2017. , p. 17
Keywords [en]
Compressive sensing, Sparsity, Bayesian hierarchical model, Matérn covariance, MRI
National Category
Probability Theory and Statistics Medical Image Processing Computational Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-141548OAI: oai:DiVA.org:umu-141548DiVA, id: diva2:1155320
Projects
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment
Funder
Swedish Research Council, 340-2013-5342Available from: 2017-11-07 Created: 2017-11-07 Last updated: 2018-06-09

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arXiv:1710.04030

Authority records BETA

Wang, JianfengZhou, ZhiyongGarpebring, AndersYu, Jun

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Wang, JianfengZhou, ZhiyongGarpebring, AndersYu, Jun
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Department of Mathematics and Mathematical StatisticsDepartment of Radiation Sciences
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CiteExportLink to record
Permanent link

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