Approximate Message Passing-based Compressed Sensing Reconstruction with Generalized Elastic Net Prior

Peer reviewed: 
Yes, item is peer reviewed.
Scholarly level: 
Faculty/Staff
Final version published as: 

Lian, Jie; Wang, Xing. Approximate Message Passing-based Compressed Sensing Reconstruction with Generalized Elastic Net Prior. Signal Processing: Image Communication 37 (2015) 19–33. doi:10.1016/j.image.2015.06.011

Date created: 
2015
Keywords: 
Compressed sensing
Approximate message passing
Elastic net prior
State evolution
Phase transition
Abstract: 

In this paper, we study the compressed sensing reconstruction problem with generalized elastic net prior (GENP), where a sparse signal is sampled via a noisy underdetermined linear observation system, and an additional initial estimation of the signal (the GENP) is available during the reconstruction. We first incorporate the GENP into the LASSO and the approximate message passing (AMP) frameworks, denoted by GENP-LASSO and GENP-AMP respectively. We then focus on GENP-AMP and investigate its parameter selection, state evolution, and noise-sensitivity analysis. A practical parameterless version of the GENP-AMP is also developed, which does not need to know the sparsity of the unknown signal and the variance of the GENP. Simulation results with 1-D data and two different imaging applications are presented to demonstrate the efficiency of the proposed schemes.

Language: 
English
Document type: 
Article
Rights: 
Copyright remains with the author. Copyright of final published version is held by Elsevier.
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Sponsor(s): 
Natural Sciences and Engineering Research Council of Canada (NSERC)
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