Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed {ℓ _1}/{ℓ _2} Regularization
Abstract
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.
- Publication:
-
IEEE Signal Processing Letters
- Pub Date:
- May 2015
- DOI:
- 10.1109/LSP.2014.2362861
- arXiv:
- arXiv:1407.5465
- Bibcode:
- 2015ISPL...22..539R
- Keywords:
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- Mathematics - Optimization and Control
- E-Print:
- 5 pages