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- Emilie Chouzenoux, Jean-Christophe Pesquet, Audrey Repetti
- J. Optimization Theory and Applications
- 2014

We consider the minimization of a function G defined on R , which is the sum of a (non necessarily convex) differentiable function and a (non necessarily differentiable) convex function. Moreover, we assume that G satisfies the KurdykaLojasiewicz property. Such a problem can be solved with the Forward-Backward algorithm. However, the latter algorithm mayâ€¦ (More)

- Emilie Chouzenoux, Jean-Christophe Pesquet, Audrey Repetti
- J. Global Optimization
- 2016

A number of recent works have emphasized the prominent role played by the KurdykaLojasiewicz inequality for proving the convergence of iterative algorithms solving possibly nonsmooth/nonconvex optimization problems. In this work, we consider the minimization of an objective function satisfying this property, which is a sum of a non necessarily convexâ€¦ (More)

- Audrey Repetti, Mai Quyen Pham, Laurent Duval, Emilie Chouzenoux, Jean-Christophe Pesquet
- IEEE Signal Process. Lett.
- 2015

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 nonsmoothâ€¦ (More)

Based on a preconditioned version of the randomized block-coordinate forward-backward algorithm recently proposed in [23], several variants of block-coordinate primal-dual algorithms are designed in order to solve a wide array of monotone inclusion problems. These methods rely on a sweep of blocks of variables which are activated at each iteration accordingâ€¦ (More)

- Guido Moerkotte, Martin J. Montag, Audrey Repetti, Gabriele Steidl
- J. Computational Applied Mathematics
- 2015

In this paper we determine the proximity functions of the sum and the maximum of componentwise (reciprocal) quotients of positive vectors. For the sum of quotients, denoted by Q1, the proximity function is just a componentwise shrinkage function which we call q-shrinkage. This is similar to the proximity function of the l1-norm which is given byâ€¦ (More)

- Audrey Repetti, Emilie Chouzenoux, Jean-Christophe Pesquet
- 2012 Proceedings of the 20th European Signalâ€¦
- 2012

This paper addresses the problem of recovering an image degraded by a linear operator and corrupted with an additive Gaussian noise with a signal-dependent variance. The considered observation model arises in several digital imaging devices. To solve this problem, a variational approach is adopted relying on a weighted least squares criterion which isâ€¦ (More)

- Alexandru Onose, Rafael E. Carrillo, +4 authors Yves Wiaux
- 2016

In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focusâ€¦ (More)

- Audrey Repetti, Emilie Chouzenoux, Jean-Christophe Pesquet
- 2015 IEEE International Conference on Acousticsâ€¦
- 2015

Primal-dual proximal optimization methods have recently gained much interest for dealing with very large-scale data sets encoutered in many application fields such as machine learning, computer vision and inverse problems [1-3]. In this work, we propose a novel random block-coordinate version of such algorithms allowing us to solve a wide array of convexâ€¦ (More)

- Audrey Repetti
- 2015

- Audrey Repetti, Emilie Chouzenoux, Jean-Christophe Pesquet
- 2015 23rd European Signal Processing Conferenceâ€¦
- 2015

The solution of many applied problems relies on finding the minimizer of a sum of smooth and/or nonsmooth convex functions possibly involving linear operators. In the last years, primal-dual methods have shown their efficiency to solve such minimization problems, their main advantage being their ability to deal with linear operators with no need to invertâ€¦ (More)