L1-Minimization Algorithm for Bayesian Online Compressed Sensing

Author(s)

Rossi, Paulo V. ^{[1, 2]} ; Vicente, Renato ^{[1, 3]}

Affiliation

^[1] Latam Experian DataLab, BR-04547130 Sao Paulo, SP - Brazil

^[2] Univ Sao Paulo, Inst Phys, Dept Gen Phys, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Sao Paulo, Inst Math & Stat, Dept Appl Math, BR-05508090 Sao Paulo, SP - Brazil

• Document type: Journal article
• Source: Entropy; v. 19, n. 12 DEC 2017.
• Web of Science Citations: 3

Abstract

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. (AU)

• FAPESP's process: 14/00792-7 - Statistical mechanics applied to compressed sensing
• Grantee: Paulo Victor Camargo Rossi
• Support Opportunities: Scholarships in Brazil - Doctorate