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Sparsity estimation...
Sparsity estimation in compressive sensing with application to MR images
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- Wang, Jianfeng (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Zhou, Zhiyong, 1989- (författare)
- Umeå universitet,Institutionen för matematik och matematisk statistik
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- Garpebring, Anders, 1980- (författare)
- Umeå universitet,Institutionen för strålningsvetenskaper
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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)
- 2017
- Engelska 17 s.
- Relaterad länk:
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https://arxiv.org/ab...
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https://urn.kb.se/re...
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Abstract
Ämnesord
Stäng
- 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.
Ämnesord
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- TEKNIK OCH TEKNOLOGIER -- Medicinteknik -- Medicinsk bildbehandling (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Medical Engineering -- Medical Image Processing (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Compressive sensing
- Sparsity
- Bayesian hierarchical model
- Matérn covariance
- MRI
- matematisk statistik
- Mathematical Statistics
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