Blind Calibration For Compressed Sensing By Convex Optimization

Rémi Gribonval 1 Gilles Chardon 2 Laurent Daudet 2
1 METISS - Speech and sound data modeling and processing
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : We consider the problem of calibrating a compressed sensing measurement system under the assumption that the decalibration consists in unknown gains on each measure. We focus on blind calibration, using measures performed on a few unknown (but sparse) signals. A naive formulation of this blind calibration problem, using l1 minimization, is reminiscent of blind source separation and dictionary learning, which are known to be highly non-convex and riddled with local minima. In the considered context, we show that in fact this formulation can be exactly expressed as a convex optimization problem, and can be solved using off-the-shelf algorithms. Numerical simulations demonstrate the effectiveness of the approach even for highly uncalibrated measures, when a sufficient number of (unknown, but sparse) calibrating signals is provided. We observe that the success/failure of the approach seems to obey sharp phase transitions.
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https://hal.inria.fr/hal-00658579
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Submitted on : Thursday, January 19, 2012 - 2:15:42 PM
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Rémi Gribonval, Gilles Chardon, Laurent Daudet. Blind Calibration For Compressed Sensing By Convex Optimization . IEEE International Conference on Acoustics, Speech, and Signal Processing, Mar 2012, Kyoto, Japan. ⟨hal-00658579v2⟩

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