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

Marylou Gabrié (1) , Jean Barbier (2) , Florent Krzakala (1) , Lenka Zdeborová (3)

1 Systèmes Désordonnés et Applications
2 ICTP - Abdus Salam International Centre for Theoretical Physics [Trieste]
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

Compressed sensing allows the acquisition of compressible signals with a small number of measurements. In experimental settings, the sensing process corresponding to the hardware implementation is not always perfectly known and may require a calibration. To this end, blind calibration proposes to perform at the same time the calibration and the compressed sensing. Schülke and collaborators suggested an approach based on approximate message passing for blind calibration (cal-AMP) in [1, 2]. Here, their algorithm is extended from the already proposed offline case to the online case, for which the calibration is refined step by step as new measured samples are received. We show that the performance of both the offline and the online algorithms can be theoretically studied via the State Evolution (SE) formalism. Finally, the efficiency of cal-AMP and the consistency of the theoretical predictions are confirmed through numerical simulations.

Mots clés: Statistical Mechanics; Disordered Systems and Neural Networks; Information Theory

Domaines: Physique [physics]

Marylou Gabrié, Jean Barbier, Florent Krzakala, Lenka Zdeborová. Blind calibration for compressed sensing: State evolution and an online algorithm. Journal of Physics A: Mathematical and Theoretical, 2020, ⟨10.1088/1751-8121/ab8416⟩. ⟨cea-02529311⟩