Blind calibration for compressed sensing: State evolution and an online algorithm

Compressed sensing, allows to acquire compressible signals with a small number of measurements. In applications, a hardware implementation often requires a calibration as the sensing process is not perfectly known. Blind calibration, that is performing at the same time calibration and compressed sen...

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Bibliographic Details
Published in:arXiv.org 2020-03
Main Authors: Gabrié, Marylou, Barbier, Jean, Krzakala, Florent, Zdeborová, Lenka
Format: Article
Language:English
Subjects:
Calibration
Compressibility
Computer simulation
Detection
Evolutionary algorithms
Message passing
Time compression
Online Access:Get full text
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Summary:Compressed sensing, allows to acquire compressible signals with a small number of measurements. In applications, a hardware implementation often requires a calibration as the sensing process is not perfectly known. Blind calibration, that is performing at the same time calibration and compressed sensing is thus particularly appealing. A potential approach was suggested by Sch\"ulke and collaborators in Sch\"ulke et al. 2013 and 2015, using approximate message passing (AMP) for blind calibration (cal-AMP). Here, the algorithm is extended from the already proposed offline case to the online case, where the calibration is refined step by step as new measured samples are received. Furthermore, we show that the performance of both the offline and the online algorithms can be theoretically studied via the State Evolution (SE) formalism. Through numerical simulations, the efficiency of cal-AMP and the consistency of the theoretical predictions are confirmed.
ISSN:2331-8422
DOI:10.48550/arxiv.1910.00285