1. Blind calibration for compressed sensing: state evolution and an online algorithm
- Author
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Jean Barbier, Florent Krzakala, Marylou Gabrié, Lenka Zdeborová, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Abdus Salam International Centre for Theoretical Physics [Trieste] (ICTP), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Additional funding is acknowledged by MG from ‘Chaire de recherche sur les modèles et sciences des données’, Fondation CFM pour la Recherche-ENS., This material is based upon work supported by Google Cloud., Support of NVIDIA Corporation with the donation of the Titan Xp GPU used for this research., ANR-17-CE23-0023,PAIL,Diagramme de Phase et Algorithme pour l'inference et l'apprentissage(2017), European Project: 714608,SMILE, Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
- Subjects
FOS: Computer and information sciences ,Statistics and Probability ,Computer science ,Calibration (statistics) ,Computer Science - Information Theory ,Information Theory ,FOS: Physical sciences ,General Physics and Astronomy ,02 engineering and technology ,01 natural sciences ,State evolution ,Statistical Mechanics ,Consistency (database systems) ,0103 physical sciences ,0202 electrical engineering, electronic engineering, information engineering ,Statistical inference ,Disordered Systems and Neural Networks ,Online algorithm ,010306 general physics ,Condensed Matter - Statistical Mechanics ,Mathematical Physics ,[PHYS]Physics [physics] ,Statistical Mechanics (cond-mat.stat-mech) ,Information Theory (cs.IT) ,Message passing ,Process (computing) ,020206 networking & telecommunications ,Statistical and Nonlinear Physics ,Disordered Systems and Neural Networks (cond-mat.dis-nn) ,Condensed Matter - Disordered Systems and Neural Networks ,Compressed sensing ,Modeling and Simulation ,Algorithm - Abstract
International audience; 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.
- Published
- 2020
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