Autocalibrated Signal Reconstruction from Linear Measurements Using Adaptive GAMP

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 $ ℓ _{ 1 } $ -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.