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Bayesian 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
2019 (English)In: Communications in Statistics: Case Studies, Data Analysis and Applications, ISSN 2373-7484Article in journal (Refereed) Epub ahead of print
Abstract [en]

The theory of compressive sensing (CS) asserts that an unknownsignal x ∈ CN can be 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. In the simulation study and real data study, magnetic resonance image data is used as input signal, which becomes sparse after sparsified transformation. The results from the simulation study confirm the theoretical properties of the estimator. In practice, the estimate from a real MR image can be used for recovering future MR images under the framework of CS if they are believed to have the same sparsity level after sparsification.

Place, publisher, year, edition, pages
Taylor & Francis Group, 2019.
Keywords [en]
Compressive sensing; sparsity; Bayesian hierarchical model; Matérn covariance; MRI
National Category
Probability Theory and Statistics Signal Processing Medical Image Processing
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-164952DOI: 10.1080/23737484.2019.1675557OAI: oai:DiVA.org:umu-164952DiVA, id: diva2:1367986
Part of project
Statistical modelling and intelligent data sampling in MRI and PET measurements for cancer therapy assessment, Swedish Research CouncilAvailable from: 2019-11-05 Created: 2019-11-05 Last updated: 2019-11-19
In thesis
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Publisher's full texthttps://www.tandfonline.com/doi/full/10.1080/23737484.2019.1675557

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Wang, JianfengGarpebring, AndersYu, Jun
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CiteExportLink to record
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  • apa
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