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Conference Papers Year : 2012

Blind Calibration For Compressed Sensing By Convex Optimization

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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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Dates and versions

hal-00658579 , version 1 (11-01-2012)
hal-00658579 , version 2 (19-01-2012)

Identifiers

  • HAL Id : hal-00658579 , version 2

Cite

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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