TY - JOUR
T1 - Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed ℓ1/ℓ2 Regularization
AU - Repetti, Audrey
AU - Pham, Mai Quyen
AU - Duval, Laurent
AU - Chouzenoux, Emilie
AU - Pesquet, Jean-Christophe
PY - 2015/5
Y1 - 2015/5
N2 - The ℓ 1 /ℓ 2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the ℓ 1 /ℓ 2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the ℓ 1 /ℓ 2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact ℓ 1 /ℓ 2 term, on an application to seismic data blind deconvolution.
AB - The ℓ 1 /ℓ 2 ratio regularization function has shown good performance for retrieving sparse signals in a number of recent works, in the context of blind deconvolution. Indeed, it benefits from a scale invariance property much desirable in the blind context. However, the ℓ 1 /ℓ 2 function raises some difficulties when solving the nonconvex and nonsmooth minimization problems resulting from the use of such a penalty term in current restoration methods. In this paper, we propose a new penalty based on a smooth approximation to the ℓ 1 /ℓ 2 function. In addition, we develop a proximal-based algorithm to solve variational problems involving this function and we derive theoretical convergence results. We demonstrate the effectiveness of our method through a comparison with a recent alternating optimization strategy dealing with the exact ℓ 1 /ℓ 2 term, on an application to seismic data blind deconvolution.
U2 - 10.1109/LSP.2014.2362861
DO - 10.1109/LSP.2014.2362861
M3 - Article
SN - 1070-9908
VL - 22
SP - 539
EP - 543
JO - IEEE Signal Processing Letters
JF - IEEE Signal Processing Letters
IS - 5
ER -