Tuesday, April 14, 2015

SOOT l1/l2 norm ratio sparse blind deconvolution - implementation -

Laurent just let me know of the release of an implementation for blind deconvolution:

Dear Igor

You have been kind enough to publicize the following paper (and you contributed to the build-up as you are indeed in the acknowledgment section featured in http://nuit-blanche.blogspot.fr/2014/07/euclid-in-taxicab-sparse-blind.html )

Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed {\ell _1}/{\ell _2} Regularization  http://dx.doi.org/10.1109/LSP.2014.2362861, http://arxiv.org/abs/1407.5465

The ℓ1/ℓ2 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 ℓ1/ℓ2 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 ℓ1/ℓ2 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 ℓ1/ℓ2 term, on an application to seismic data blind deconvolution.

After a little delay, the code is made available at Matlab Central:


but also here:


just a few days before its presentation at ICASSP 2015 in Brisbane, Australia


Thank you


Laurent Duval
IFP Energies nouvelles - Direction Mécatronique et Numérique
Thanks Laurent !
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