@Article{Repetti_A_2015_j-ieee-spl_euclid_tsbdsl1l2r,
  author    = {A. Repetti and M. Q. Pham and L. Duval and E. Chouzenoux and J.-C. Pesquet},
  title     = {Euclid in a Taxicab: Sparse Blind Deconvolution with Smoothed $\ell_1/\ell_2$ Regularization},
  year      = {2015},
  journal   = {IEEE Signal Processing Letters},
  doi       = {10.1109/LSP.2014.2362861},
  volume    = {22},
  number    = {5},
  pages     = {539--543},
  eprint    = {1407.5465},
  url       = {http://dx.doi.org/10.1109/LSP.2014.2362861},
  month     = {May},
  abstract  = {The ${ell _1}/{ell _2}$ 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 ${ell _1}/{ell _2}$ 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 ${ell _1}/{ell _2}$ 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 ${ell _1}/{ell _2}$ term, on an application to seismic data blind deconvolution.},
  timestamp = {2015.03.21.00.44},
}