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Bayesian sparsity e...
Bayesian sparsity estimation in compressive sensing with application to MR images
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- Wang, Jianfeng, 1984- (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Zhou, Zhiyong (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Garpebring, Anders (författare)
- Umeå universitet,Radiofysik
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- Yu, Jun, 1962- (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik,Mathematical Statistics
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(creator_code:org_t)
- 2019-11-05
- 2019
- Engelska.
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Ingår i: Communications in Statistics: Case Studies, Data Analysis and Applications. - : Taylor & Francis Group. - 2373-7484. ; 5:4, s. 415-431
- Relaterad länk:
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Signalbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Signal Processing (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Medical Engineering -- Medical Image Processing (hsv//eng)
Nyckelord
- Compressive sensing
- sparsity
- Bayesian hierarchical model
- Matérn covariance
- MRI
- matematisk statistik
- Mathematical Statistics
Publikations- och innehållstyp
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- art (ämneskategori)
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