TY - GEN
T1 - Optimization of a Geman-McClure like criterion for sparse signal deconvolution
AU - Castella, Marc
AU - Pesquet, Jean Christophe
N1 - Publisher Copyright:
© 2015 IEEE.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - This paper deals with the problem of recovering a sparse unknown signal from a set of observations. The latter are obtained by convolution of the original signal and corruption with additive noise. We tackle the problem by minimizing a least-squares fit criterion penalized by a Geman-McClure like potential. The resulting criterion is a rational function, which makes it possible to formulate its minimization as a generalized problem of moments for which a hierarchy of semidefinite programming relaxations can be proposed. These convex relaxations yield a monotone sequence of values which converges to the global optimum. To overcome the computational limitations due to the large number of involved variables, a stochastic block-coordinate descent method is proposed. The algorithm has been implemented and shows promising results.
AB - This paper deals with the problem of recovering a sparse unknown signal from a set of observations. The latter are obtained by convolution of the original signal and corruption with additive noise. We tackle the problem by minimizing a least-squares fit criterion penalized by a Geman-McClure like potential. The resulting criterion is a rational function, which makes it possible to formulate its minimization as a generalized problem of moments for which a hierarchy of semidefinite programming relaxations can be proposed. These convex relaxations yield a monotone sequence of values which converges to the global optimum. To overcome the computational limitations due to the large number of involved variables, a stochastic block-coordinate descent method is proposed. The algorithm has been implemented and shows promising results.
U2 - 10.1109/CAMSAP.2015.7383798
DO - 10.1109/CAMSAP.2015.7383798
M3 - Conference contribution
AN - SCOPUS:84963815677
T3 - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
SP - 309
EP - 312
BT - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
Y2 - 13 December 2015 through 16 December 2015
ER -