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Autocalibrated Signal Reconstruction from Linear Measurements Using Adaptive GAMP

U.S. Kamilov, A. Bourquard, E. Bostan, M. Unser

Proceedings of the Thirty-Eighth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'13), Vancouver BC, Canada, May 26-31, 2013, pp. 5925-5928.

In this paper, we reconstruct signals from underdetermined linear measurements where the componentwise gains of the measurement system are unknown a priori. The reconstruction is performed through an adaptation of the message-passing algorithm called adaptive GAMP that enables joint gain calibration and signal estimation. To evaluate our approach, we apply it to the problem of sparse recovery and compare it against an ℓ1-based approach. We numerically show that adaptive GAMP yields excellent results even for a moderate amount of data. It approaches the performance of oracle GAMP where the gains are perfectly known asymptotically.

AUTHOR="Kamilov, U.S. and Bourquard, A. and Bostan, E. and Unser, M.",
TITLE="Autocalibrated Signal Reconstruction from Linear Measurements
        Using Adaptive {GAMP}",
BOOKTITLE="Proceedings of the Thirty-Eighth {IEEE} International
        Conference on Acoustics, Speech, and Signal Processing
address="Vancouver BC, Canada",
month="May 26-31,",

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