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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Bibliographic Details
Main Authors: Cao, Jiuwen, Lin, Zhiping
Other Authors: School of Electrical and Electronic Engineering
Format: Conference or Workshop Item
Language:English
Published: 2013
Subjects:
Online Access:https://hdl.handle.net/10356/103144
http://hdl.handle.net/10220/16909
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Institution: Nanyang Technological University
Language: English
Description
Summary: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.