Bayesian Compressive Sensing Using Laplace Priors

In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the spars...

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Bibliographic Details
Published in:IEEE transactions on image processing Vol. 19; no. 1; pp. 53 - 63
Main Authors: Babacan, S.D., Molina, R., Katsaggelos, A.K.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2010
Institute of Electrical and Electronics Engineers
Subjects:
Algorithm design and analysis
Applied sciences
Bayesian methods
compressive sensing
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Image coding
Image processing
Image reconstruction
Image sampling
Image sensors
Information, signal and communications theory
inverse problems
Reconstruction algorithms
relevance vector machine (RVM)
Signal and communications theory
Signal processing
Signal sampling
Signal, noise
sparse Bayesian learning
Telecommunications and information theory
Time measurement
Bayes estimation
Performance evaluation
State of the art
Vector method
Inverse problem
Learning
relevance vector machine (RVM)
Acquisition process
Relevance criterion
Bayesian methods
inverse problems
Greedy algorithm
Bayes methods
Signal detection
compressive sensing
sparse Bayesian learning
User need
ISSN:1057-7149, 1941-0042, 1941-0042
Online Access:Get full text
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Summary:In this paper, we model the components of the compressive sensing (CS) problem, i.e., the signal acquisition process, the unknown signal coefficients and the model parameters for the signal and noise using the Bayesian framework. We utilize a hierarchical form of the Laplace prior to model the sparsity of the unknown signal. We describe the relationship among a number of sparsity priors proposed in the literature, and show the advantages of the proposed model including its high degree of sparsity. Moreover, we show that some of the existing models are special cases of the proposed model. Using our model, we develop a constructive (greedy) algorithm designed for fast reconstruction useful in practical settings. Unlike most existing CS reconstruction methods, the proposed algorithm is fully automated, i.e., the unknown signal coefficients and all necessary parameters are estimated solely from the observation, and, therefore, no user-intervention is needed. Additionally, the proposed algorithm provides estimates of the uncertainty of the reconstructions. We provide experimental results with synthetic 1-D signals and images, and compare with the state-of-the-art CS reconstruction algorithms demonstrating the superior performance of the proposed approach.
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ISSN:1057-7149
1941-0042
1941-0042
DOI:10.1109/TIP.2009.2032894