TY - GEN
T1 - Blind Calibration for Sparse Regression
T2 - 8th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019
AU - Gabrie, Marylou
AU - Barbier, Jean
AU - Krzakala, Florent
AU - Zdeborova, Lenka
N1 - Publisher Copyright:
© 2019 IEEE.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Sparse regression, such as the one used in compressed sensing, allows to acquire compressible signals with a small number of measurements. As such, a correct calibration of a potential hardware problem is a central issue. Blind calibration, that is performing at the same time calibration and compressed sensing when the training signals are sparse but unknown, is thus particularly appealing. A potential approach was suggested by Schülke et al, using an approximate message passing (AMP) for blind calibration (cal-AMP). Here, we show that the asymptotic performances of this algorithm can be analysed by an exact state evolution equation. It allows to confirm that cal-AMP requires a smaller number of measurements and/or signals in order to perform with respect to standard convex approaches, and opens the way to more complex message passing techniques.
AB - Sparse regression, such as the one used in compressed sensing, allows to acquire compressible signals with a small number of measurements. As such, a correct calibration of a potential hardware problem is a central issue. Blind calibration, that is performing at the same time calibration and compressed sensing when the training signals are sparse but unknown, is thus particularly appealing. A potential approach was suggested by Schülke et al, using an approximate message passing (AMP) for blind calibration (cal-AMP). Here, we show that the asymptotic performances of this algorithm can be analysed by an exact state evolution equation. It allows to confirm that cal-AMP requires a smaller number of measurements and/or signals in order to perform with respect to standard convex approaches, and opens the way to more complex message passing techniques.
KW - Belief propagation
KW - Compressed sensing
KW - approximate message passing
KW - blind calibration
U2 - 10.1109/CAMSAP45676.2019.9022479
DO - 10.1109/CAMSAP45676.2019.9022479
M3 - Conference contribution
AN - SCOPUS:85082397211
T3 - 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings
SP - 649
EP - 653
BT - 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2019 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 15 December 2019 through 18 December 2019
ER -