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Open AccessArticle

L1-Minimization Algorithm for Bayesian Online Compressed Sensing

by Paulo V. Rossi 1,2,* and Renato Vicente 1,3
1
Latam Experian DataLab , São Paulo-SP 04547-130, Brazil
2
Department of General Physics, Institute of Physics, University of São Paulo, São Paulo-SP 05508-090, Brazil
3
Department of Applied Mathematics, Institute of Mathematics and Statistics, University of São Paulo, São Paulo-SP 05508-090, Brazil
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 667; https://doi.org/10.3390/e19120667
Received: 3 November 2017 / Revised: 25 November 2017 / Accepted: 1 December 2017 / Published: 5 December 2017
In this work, we propose a Bayesian online reconstruction algorithm for sparse signals based on Compressed Sensing and inspired by L1-regularization schemes. A previous work has introduced a mean-field approximation for the Bayesian online algorithm and has shown that it is possible to saturate the offline performance in the presence of Gaussian measurement noise when the signal generating distribution is known. Here, we build on these results and show that reconstruction is possible even if prior knowledge about the generation of the signal is limited, by introduction of a Laplace prior and of an extra Kullback–Leibler divergence minimization step for hyper-parameter learning. View Full-Text
Keywords: compressed sensing; L1-minimization; online learning; Bayesian inference compressed sensing; L1-minimization; online learning; Bayesian inference
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Rossi, P.V.; Vicente, R. L1-Minimization Algorithm for Bayesian Online Compressed Sensing. Entropy 2017, 19, 667.

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