Institut de Mathématiques de Toulouse

Accueil > Événements Scientifiques > Séminaires & Groupes de Travail > Anciens Séminaires > CIMI - Image Processing Seminar

CIMI - Image Processing Seminar

par Delphine Dallariva - publié le , mis à jour le




  • Lundi 6 mai 2013 14:00-15:00 - Frédéric Pascal

    Robust covariance matrices estimation and applications to SAR and Hyperspectral images processing

    Résumé : This talk deals with problems of covariance matrix estimation in radar/signal processing. Under the widely used Gaussian assumption, the Sample Covariance Matrix (SCM) estimate provides optimal results in terms of estimation performance. However, when the data turn to be non-Gaussian, the resulting performance can be strongly degraded. To fill this gap, I will first introduce the general framework of the Robust Estimation Theory : elliptical distributions and M-estimators and their statistical performance. Then, I will show some recent results, applied to classification problems in polarimetric SAR images as well as detection problems in Hyperspectral images.

    Lieu : ENSEEIHT, Salle B105


  • Lundi 6 mai 2013 15:30-16:30 - Stéphanie Allassonnière

    L’anatomie numérique : un enjeu mathématique

    Lieu : ENSEEIHT, Salle B105


  • Lundi 13 mai 2013 14:00-15:00 - Jean-François Giovannelli

    Pénalisation L2+L1 et algorithme ADMM en synthèse de Fourier et application à la radio-héliographie

    Résumé : Le travail présenté est motivé par une application en radio-héliographie (imagerie du soleil dans les longueurs d’onde radio) par interférométrie (à partir d’un réseau d’antenne). Cet instrument mesure des coefficients de Fourier bruités de l’objet inconnu sur une grille incomplète et la reconstruction des images pose donc un problème de synthèse de Fourier. Par ailleurs, les objets d’intérêt présentent la particularité de posséder une composante impulsionnelle et une composante étendue superposées. Nous présentons une méthode permettant la reconstruction de deux cartes reposant sur une double pénalité convexe : un terme L1 pour la composante impulsionnelle et un terme de L2 pour la composante étendue. A cela s’ajoutent des contraintes de positivité et de support. L’optimisation repose sur un algorithme de lagrangien augmenté et une descente de alternée (ADMM). Les résultats présentés montrent les capacités à la fois de séparation des deux composantes et de sur-résolution de la composante impulsionnelle.
    Le travail est publié dans J.-F. Giovannelli and A. Coulais, "Positive deconvolution for superimposed extended sources and point sources", Astronomy and astrophysics, vol. 439, pp. 401-412, 2005 et il est disponible là : http://giovannelli.free.fr/Papers/AetAParu.pdf

    Lieu : ENSEEIHT, Salle B105


  • Lundi 13 mai 2013 15:00-16:00 - Nelly Pustelnik

    Epigraphical Projection and Proximal Tools for Solving Constrained Convex Optimization Problems

    Résumé : We propose a proximal approach to deal with a class of convex optimization problems involving nonlinear constraints. A large family of such constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower level set of a sum of convex functions evaluated over different, but possibly overlapping, blocks of the signal. For such constraints, the associated projection operator generally does not have a simple form. We circumvent this difficulty by splitting the lower level set into as many epigraphs as functions involved in the sum. A closed half-space constraint is also enforced, in order to limit the sum of the introduced epigraphical variables to the upper bound of the original lower level set.
    In this presentation, we focus on a family of constraints involving linear transforms of distance functions to a convex set or l_1,p norms with p=2 or p=+infty. In these cases, the projection onto the epigraph of the involved function has a closed form expression.
    The proposed approach is validated in the context of image restoration
    with missing samples, by making use of TV-like constraints. Experiments
    show that our method leads to significant improvements in term of convergence speed over existing algorithms for solving similar constrained problems.

    Lieu : ENSEEIHT, Salle B105


  • Mardi 21 mai 2013 14:00-15:00 - Jalal Fadili

    Stable Recovery with Sparse Analysis Regularization

    Résumé : This work investigates the theoretical guarantees of l1-analysis regularization when solving linear inverse problems. Most of previous works in the literature have mainly focused on the sparse synthesis prior where the sparsity is measured as the l1 norm of the coefficients that synthesize the signal from a given dictionary. In contrast, the more general analysis regularization minimizes the l1 norm of the correlations between the signal and the atoms in the dictionary. The corresponding variational problem encompasses several well-known regularizations such as the discrete total variation and the Fused Lasso. We give a sufficient condition to ensure that a signal is the unique solution of the l1-analysis regularization in the noiseless case. The same condition also guarantees exact analysis support recovery and l2-robustness of the l1-analysis minimizer vis-à-vis an enough small noise in the measurements. This condition turns to be sharp for the robustness of the sign pattern. To show partial support recovery and l2-robustness to an arbitrary bounded noise, we introduce a stronger sufficient condition. When specialized to the l1-synthesis regularization, our results recover some corresponding recovery and robustness guarantees previously known in the literature. From this perspective, our work is a generalization of these results. We finally illustrate these theoretical findings on several examples to study the robustness of the 1-D total variation, shift-invariant Haar and Fused Lasso regularizations.
    Joint work with S. Vaiter, G. Peyré and C. Dossal.

    Lieu : IMT


  • Mardi 21 mai 2013 15:30-16:30 - Jalal Fadili

    Stable Recovery with Analysis Decomposable Priors

    Résumé : In this paper, we investigate in a unified way the structural properties of solutions to inverse problems. These solutions are regularized by the generic class of semi-norms defined as a decomposable norm composed with a linear operator, the so-called analysis type decomposable prior. This encompasses several well-known analysis-type regularizations such as the discrete total variation (in any dimension), analysis group-Lasso or the nuclear norm. Our main results establish sufficient conditions under which uniqueness and stability to a bounded noise of the regularized solution are guaranteed. Along the way, we also provide a necessary and sufficient uniqueness result that is of independent interest and goes beyond the case of decomposable norms.
    Joint work with G. Peyré, S. Vaiter, C.-A. Deledalle and J. Salmon.

    Lieu : IMT


  • Lundi 17 juin 2013 14:00-15:00 - Jean-François Aujol

    Modélisation des textures

    Résumé : Dans cet exposé, on s’intéressera à la modélisation mathématiques des textures. On considérera la définition de texture comme élément oscillant donnée par Yves Meyer, et on comparera à une approche plus géométrique. Notre étude sera guidée par le problème de décomposition d’images en géométrie et texture.

    Lieu : IMT, Salle de Conf. MIP, Bât. 1R3


  • Lundi 17 juin 2013 15:30-16:30 - Jose Bioucas-Dias

    Alternating Direction Optimization for Convex Inverse Problems

    Résumé : In this talk I will address a new class of fast of algorithms for solving convex inverse problems where the objective function is a sum of convex terms with possibly convex constraints. Usually, one of terms in the objective function measures the data fidelity while the others, jointly with the constraints, enforce some type of regularization on the solution.
    Several particular features of these problems (e.g., huge dimensionality and nonsmoothness) preclude the use of off-the-shelf optimization tools and have stimulated a considerable amount of research. In this talk, I will present a new class of algorithms to handle convex inverse problems tailored to image recovery applications. The proposed class of algorithms is an instance of the so-called alternating direction method of multipliers (ADMM), for which convergence sufficient conditions are known. We show that these conditions are satisfied by the proposed class of algorithms.
    The effectiveness of the proposed approach is illustrated in a series of imaging inverse problems, including deconvolution, reconstruction from compressive observations, and sparse hyperspectral unmixing.

    Lieu : IMT, Salle de Conf. MIP, Bât. 1R3


  • Lundi 1er juillet 2013 14:00-15:00 - Fredrik Andersson

    Alternating direction methods for frequency estimation and approximation by sums of exponentials

    Résumé : Parametric high-resolution method for the estimation of the frequency nodes of linear combinations of complex exponentials with exponential damping are discussed. Kronecker’s theorem will be used to formulate the associated nonlinear least squares problem as an optimization problem in the space of vectors generating Hankel matrices of fixed rank. Approximate solutions to this problem are obtained by using the alternating direction method of multipliers. Finally, frequency estimates can be extracted from the con-eigenvectors of the solution Hankel matrix. The resulting algorithm is simple, easy to implement and can be applied to data with equally spaced samples with approximation weights, which for instance allows cases of missing data samples

    Lieu : IMT, Salle de Conf. MIP, Bât. 1R3


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