The detection bound of the probability of error in compressed sensing using Bayesian approach

In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical...

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Main Authors: Cao, Jiuwen, Lin, Zhiping
Other Authors: School of Electrical and Electronic Engineering
Format: Conference or Workshop Item
Language:English
Published: 2013
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Online Access:https://hdl.handle.net/10356/103144
http://hdl.handle.net/10220/16909
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Institution: Nanyang Technological University
Language: English
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spelling sg-ntu-dr.10356-1031442020-03-07T13:24:51Z The detection bound of the probability of error in compressed sensing using Bayesian approach Cao, Jiuwen Lin, Zhiping School of Electrical and Electronic Engineering IEEE International Symposium on Circuits and Systems (2012 : Seoul, Korea) DRNTU::Engineering::Electrical and electronic engineering In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result. 2013-10-25T03:58:48Z 2019-12-06T21:06:27Z 2013-10-25T03:58:48Z 2019-12-06T21:06:27Z 2012 2012 Conference Paper Cao, J., & Lin, Z. (2012). The detection bound of the probability of error in compressed sensing using Bayesian approach. 2012 IEEE International Symposium on Circuits and Systems, 2577-2580. https://hdl.handle.net/10356/103144 http://hdl.handle.net/10220/16909 10.1109/ISCAS.2012.6271831 en © 2012 IEEE
institution Nanyang Technological University
building NTU Library
country Singapore
collection DR-NTU
language English
topic DRNTU::Engineering::Electrical and electronic engineering
spellingShingle DRNTU::Engineering::Electrical and electronic engineering
Cao, Jiuwen
Lin, Zhiping
The detection bound of the probability of error in compressed sensing using Bayesian approach
description In this paper, we consider the theoretical bound of the probability of error in compressed sensing (CS) with the Bayesian approach. In the detection problem, the signal is sparse and is reconstructed from a compressed measurement vector. Utilizing the oracle estimator in CS, we provide a theoretical bound of the probability of error when the noise in CS is white Gaussian noise (WGN). We show that without any additional information in CS, the probability of error obtained using the signal reconstructed by four recovery algorithms: the basis pursuit denoising (BPDN) algorithm, the Dantzig selector, the orthogonal matching pursuit (OMP) method and the compressive sampling matching pursuit (CoSaMP) algorithm is always larger than the derived theoretical bound. Simulation results demonstrate the effectiveness of our result.
author2 School of Electrical and Electronic Engineering
author_facet School of Electrical and Electronic Engineering
Cao, Jiuwen
Lin, Zhiping
format Conference or Workshop Item
author Cao, Jiuwen
Lin, Zhiping
author_sort Cao, Jiuwen
title The detection bound of the probability of error in compressed sensing using Bayesian approach
title_short The detection bound of the probability of error in compressed sensing using Bayesian approach
title_full The detection bound of the probability of error in compressed sensing using Bayesian approach
title_fullStr The detection bound of the probability of error in compressed sensing using Bayesian approach
title_full_unstemmed The detection bound of the probability of error in compressed sensing using Bayesian approach
title_sort detection bound of the probability of error in compressed sensing using bayesian approach
publishDate 2013
url https://hdl.handle.net/10356/103144
http://hdl.handle.net/10220/16909
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