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
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: 2019-11-20
In thesis
1. Enhanced block sparse signal recovery and bayesian hierarchical models with applications
Open this publication in new window or tab >>Enhanced block sparse signal recovery and bayesian hierarchical models with applications
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis is carried out within two projects ‘Statistical modelling and intelligentdata sampling in Magnetic resonance imaging (MRI) and positron-emission tomography(PET) measurements for cancer therapy assessment’ and ‘WindCoE -Nordic Wind Energy Center’ during my PhD study. It mainly focuses on applicationsof Bayesian hierarchical models (BHMs) and theoretical developments ofcompressive sensing (CS). Under the first project, Paper I improves the quantityestimation of MRI parametric imaging by utilizing inherent dependent structure inthe image through BHMs; Paper III constructs a theoretically unbiased and asymptoticallynormal estimator of sparsity of a sparsified MR image by using a BHM;Paper IV extends block sparsity estimation from real-valued signal recovery tocomplex-valued signal recovery. It also demonstrates the importance of accuratelyestimating the block sparsity through a sensitivity analysis; Paper V proposes anew measure, i.e. q-ratio block constrained minimal singular value, of measurementmatrix for block sparse signal recovery. An algorithm for computing thisnew measure is also presented. In the second project, Paper II estimates the uncertaintyof Weather Research and Forecasting (WRF) model’s daily-mean 2-metertemperature in a cold region by using a BHM. It is a computationally cheaper andfaster alternative to traditional ensemble approach. In summary, this thesis makessignificant contributions in improving and optimizing the estimation proceduresof parameters of interest in MRI and WRF in practice, and developing the novelestimators and measure under the framework of CS in theory.

Place, publisher, year, edition, pages
Umeå: Umeå University, 2019. p. 35
Series
Research report in mathematical statistics, ISSN 1653-0829 ; 69
Keywords
Magnetic resonance imaging, Bayesian hierarchical models, Weather Research and Forecasting, Compressive sensing, Block sparsity, Multivariate isotropic symmetric a-stable distribution, q-ratio block constrained minimal singular value
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:umu:diva-165285 (URN)978-91-7855-148-4 (ISBN)
Public defence
2019-12-17, N450, Naturvetarhuset, Umeå University, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2019-11-26 Created: 2019-11-19 Last updated: 2019-11-26Bibliographically approved

Open Access in DiVA

fulltext(2571 kB)6 downloads
File information
File name FULLTEXT01.pdfFile size 2571 kBChecksum SHA-512
fb1e5a247dd8e17fd04a2556c379651b988df3cabbdd826c5fc6228553597eabf077cede7cbdc14c4c61b743a8875d147028005c80f577e41e08b0b86738e706
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Search in DiVA

By author/editor
Wang, JianfengZhou, ZhiyongGarpebring, AndersYu, Jun
By organisation
Department of Mathematics and Mathematical StatisticsDepartment of Radiation Sciences
Probability Theory and StatisticsSignal ProcessingMedical Image Processing

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: 42 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