Organisée par SMAI-SIGMA, groupe thématique de la Société de Mathématiques Appliquées et Industrielles (SMAI), cette rencontre annuelle a pour objectif de rassembler la communauté française autour des thémes Signal, Image, Géométrie Algorithmique, Modélisation Géométrique, et Approximation. Cette année, la journée a été préparée en collaboration avec les GDR MOA et MSPC ainsi que le laboratoire JLL. Parmi les sept exposés de niveau accessible pour non-experts, trois exposés de l'après-midi seront axés sur le sujet parcimonie en signal et image.

Programme

La journée comportera sept communications orales d'une durée de 40 minutes plus 5 minutes de discussion. Cliquer sur un titre pour voir le résumé de l'exposé.

Horaire	Salle (Couloir)	Conférencier et titre de l'exposé
09:30-10:15	309 (15-16)	François-Xavier Vialard (Dauphine) : Geodesic regression and cubic splines on shape spaces [ Slides | Filme1 | Filme2 | Filme3 ]
10:15-10:45		pause café (salle café en face de la salle 309 (15-16))
10:45-11:30	309 (15-16)	Nelly Pustelnik (Bordeaux) : Proximal methods for constrained cosparse modelling [ Slides ]
11:30-12:15	309 (15-16)	Steve Oudot (INRIA Saclay) : Unsupervised Learning using Topological Persistence [ Slides ]
12:15-13:45		pause midi (buffet sur place) (salle café en face de la salle 309 (15-16))
13:45-14:15	326 (15-25)	AG SMAI-SIGMA (ouverte à tous)
14:15-15:00	326 (15-25)	Daniel Kressner (EPF Lausanne) : Low-rank matrix and tensor techniques in scientific computing
15:00-15:45	326 (15-25)	Rémi Gribonval (INRIA Rennes) : Sparsity & Co.: Analysis vs Synthesis in Low-Dimensional Signal Models [ Slides ]
15:45-16:15		pause café (salle café en face de la salle 309 (15-16))
16:15-17:00	326 (15-25)	Laurent Condat (Caen) : Modèles et méthodes pour l'acquisition des images couleurs matricées [ Slides ]
17:00-17:45	326 (15-25)	Stephen Becker (Laboratoire JLL, Paris VI) : TFOCS: A General First-Order Framework for Solving Constrained Optimization [ Slides ]

Inscription

L'inscription est gratuite mais obligatoire. Veuillez remplir ce formulaire, la liste des participants sera mise à jour ultérieurement.

Lieu de la rencontre

La Journée scientifique SMAI-SIGMA aura lieu à l'Université Pierre et Marie Curie - Paris VI, 4 Place Jussieu, 75005 Paris, Metro Jussieu. Plan d'accès pour l'université.

Les exposés se déroulent le matin en salle 309, couloir 15-16, et l'après-midi en salle 326, couloir 15-25, toutes les deux au troisième étage. Les pauses se déroulent dans une salle café en face de la salle 309.

Liste de participants

Stephen Becker		Laboratoire JLL, Paris VI
Laurent Condat		GREYC, Image team, Caen
Rémi Gribonval		INRIA Rennes
Daniel Kressner		ANCHP, EPF Lausanne
Steve Oudot		INRIA Saclay
Nelly Pustelnik		IMS, Bordeaux
François-Xavier Vialard	CEREMADE, Université Paris-Dauphine
Marie-Laurence Mazure	Laboratoire Jean Kuntzmann, Université Joseph Fourier, Grenoble 
Bang Cong Vu		Laboratoire Jacques-Louis Lions, Paris 6
Frederic Nataf		LJLL
Jean-Marie Mirebeau	Ceremade, Université Paris-Dauphine
Patrice Brault		LSS Laboratoire des Signaux et Systemes, CNRS UMR8506/ Supelec/ U-Psud
Jerôme Bobin		CEA
Valérie Perrier		Laboratoire Jean Kuntzmann, Grenoble INP
Cécile Louchet		Laboratoire MAPMO, Université d'Orléans
Eric Nyiri		Arts et Métiers ParisTech
Yannick Kergosien	LIM&BIO, Université Paris13
Frédéric Chazal		INRIA Saclay
Christian Gout		LMI, INSA de Rouen
Alexandre Bos		INRIA Saclay
Christophe Rabut	Université de Toulouse (INSA, IMT, IREM)
Anna Jezierska		Université Paris-Est, Institut Gaspard Monge
Emilie Chouzenoux	LIGM, Université Paris Est Marne-La-Vallée
Caroline Chaux		LIGM UMR CNRS 8049
Ana Matos		Université de Lille 1
Patrick Chenin		Laboratoire LJK Université de Grenoble (UJF)
Louie John VALLEJO	Laboratoire Jacques-Louis Lions, Paris VI / Universite des Philippines
Giap Nguyen		Laboratoire L3i, Université de La Rochelle
Laurent Duval		IFP Energies nouvelles
Andrés ALMANSA		CNRS LTCI - Telecom ParisTech
Laurent Sifre		Ecole Polytechnique
Gérard Chollet		CNRS-LTCI, TELECOM-ParisTech
Thomas Oberlin		Laboratoire Jean Kuntzmann
El Hadji Diop		CMM, Mines Paris Tech
Samuel Vaiter		CEREMADE
Dominique Pastor	Lab-STICC Télcom Bretagne
Georgios Tzagkarakis	CEA, IRFU/SEDI
Hugo Raguet		CEREMADE
Eva Wesfreid		CMLA, ENS Cachan
Moulay Abdellah Chkifa	UPMC
Rachel ABABOU 		Ecoles de Saint-Cyr Coëtquidan
Alain PERRONNET		LJLL UPMC
Giovanni Chierchia	TSI, Telecom Paris-Tech
Jean-Francois Cardoso	LTCI CNRS & IAP
Laurent Gajny		LSIS - Arts et Métiers ParisTech
Nicolas Schmidt		CEREMADE
Fernand Meyer		Mines-ParisTech
Charles-Alban Deledalle	CEREMADE, Paris Dauphine
Bernhard Beckermann	Labo Painlevé, Université de Lille 1
Albert Cohen		Laboratoire JLL, Paris VI
Patrick Louis Combettes	Laboratoire JLL, Paris VI
Gabriel Peyré		Ceremade, Université Paris-Dauphine
...

Les organisateurs

• Bernhard Beckermann, Laboratoire Paul Painlevé, Université des Sciences et Technologies de Lille
• Albert Cohen, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
• Patrick Louis Combettes, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris
• Gabriel Peyré, CEREMADE, Université Paris-Dauphine

Sponseurs de la rencontre

SMAI-SIGMA, groupe thématique de la SMAI
GDR Mathématiques des systèmes perceptifs et cognitifs (MSPC)
GDR Mathématiques de l'Optimisation et Applications (MOA)
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris

Résumés des exposés

Stephen Becker (Laboratoire JLL, Paris VI) : TFOCS: A General First-Order Framework for Solving Constrained Optimization

There are many specialized solvers that solve very specific convex programs efficiently, but there are few algorithms that are general and can deal with complicated constraints. To address this and other problems, we introduce a framework and software package called TFOCS. The method relies on two tricks: dualization and smoothing. This talk describes the framework and also discusses recent splitting methods such as the method by Chambolle and Pock.

Laurent Condat (Caen) : Modèles et méthodes pour l'acquisition des images couleurs matricées

Les images couleurs sont acquises dans les appareils photo au moyen d’un capteur unique sur lequel une matrice de filtres couleurs (CFA) est superposée. Le problème de dématriçage/débruitage conjoint consiste à reconstruire une image couleurs à partir des données brutes délivrées par le capteur. Nous étudions les problématiques liées au choix du CFA et à la reconstruction des images couleurs et proposons quelques solutions, dont les résultats représentent l'état de l'art.

Rémi Gribonval (INRIA Rennes) : Sparsity & Co.: Analysis vs Synthesis in Low-Dimensional Signal Models

In the past decade there has been a great interest in a synthesis-based model for signals, based on sparse and redundant representations. Such a model, which assumes that the signal of interest can be composed as a linear combination of few columns from a given matrix (the dictionary), has been extensively exploited in signal and image processing. Its applications range from compression, denoising, deblurring & deconvolution, to blind signal separation, and even more recently to new approaches to acquire and measure data with the emerging paradigm of compressive sensing. The talk will begin with a brief review of the main existing algorithmic and theoretical results dedicated to the recovery of sparse vectors from low-dimensional projections, which form the basis of a number of signal reconstruction approaches for such generic linear inverse problems (e.g., compressed sensing, inpainting, source separation, etc.).
An alternative analysis-based model can be envisioned, where an analysis operator multiplies the signal, leading to a so-called cosparse outcome. How similar are the two signal models ? Can one derive cosparse regularization algorithms with performance guarantees when the data to be reconstructed is cosparse rather than sparse ? Existing empirical evidence in the litterature suggests that a positive answer is likely. In recent work we propose a uniqueness result for the solution of linear inverse problems under a cosparse hypothesis, based on properties of the analysis operator and the measurement matrix. Unlike with the synthesis model, where recovery guarantees usually require the linear independence of sets of few columns from the dictionary, our results suggest that linear dependencies between rows of the analysis operators may be desirable. The nature and potential of these new results will be discussed and illustrated with toy image processing and acoustic imaging experiments (joint work with S. Nam, M. Davies and M. Elad).

Daniel Kressner (EPF Lausanne) : Low-rank matrix and tensor techniques in scientific computing

Matrices with (approximate) low rank structure have played a pivotal role in the development of fast solvers in numerical linear algebra. Recently, significant progress has been made in extending these ideas to tensors. Nowadays, low-rank tensor techniques have been applied to a wide range of problems, including the solution of high-dimensional, parameter-dependent PDEs and the simulation of quantum many-body systems. This talk aims at providing a survey of these developments, focussing on the use of multivariate approximations for analysing the accuracy and convergence of algorithms based on low-rank tensors.

Steve Oudot (Saclay) : Unsupervised Learning using Topological Persistence

In this talk I will present a clustering scheme that combines a mode-seeking phase with a cluster merging phase in the corresponding density map. While mode detection is done by a standard graph-based hill-climbing scheme, the novelty of the proposed approach resides in its use of topological persistence to guide the merging of clusters. The algorithm provides additional feedback in the form of a set of points in the plane, called a persistence diagram, which provably reflects the prominences of the modes of the density. In practice, this feedback enables the user to choose relevant parameter values, so that under mild sampling conditions the algorithm will output the correct number of clusters, a notion that can be made formally sound within persistence theory. After presenting the algorithm and showing some experimental data, I will move on to the theory and introduce topological persistence together with its most fundamental result: the stability of persistence diagrams.

Nelly Pustelnik (Bordeaux) : Proximal methods for constrained cosparse modelling

The concept of cosparsity has been recently introduced in the arena of compressed sensing. It consists of minimizing the l0 norm (or the l1 norm) of an analysis-based representation of the target signal under a data fidelity constraint. The main contribution of this work is the introduction of a new projection technique, which allows us to consider more flexible data fidelity constraints than the standard quadratic one. The validity of our approach is illustrated through an application to image restoration in the presence of Poisson noise. (work in collaboration with G. Chierchia, J.-C. Pesquet, and B. Pesquet-Popescu)

François-Xavier Viallard (Ceremade, Université Dauphine) : Geodesic regression and cubic splines on shape spaces

After a brief introduction to our target applications in biomedical imaging, we present the generalisation of two standard mathematical tools to the space of shapes in a diffeomorphic framework, namely linear regression and cubic splines. These two generalizations have very different goals that are both motivated by the quantitative and statistical study of time sequences of shapes (for which the time sampling is relatively sparse) which is a subject of growing interest in the biomedical imaging community. The mathematical tools involved are riemannian geometry infinite dimension and simple optimal control tools.