H 1 Low complexity regularization of inverse problem - Recovery guarantees

Auteurs : Peyré, Gabriel (Auteur de la Conférence)
CIRM (Editeur )

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convex optimization impact of the noise linear model - sparsity structured sparsity total variation low rank gauge function L1 norm nuclear form subdifferential L1 example nuclear norm example dual certificate noise robustness compressed sensing phase transition minimal-norm certificate model stability compressed sensing sparse deconvolution regularization with measures optimization over measures space support stability example : low-pass filter

Résumé : In this talk, we investigate in a unified way the structural properties of a large class of convex regularizers for linear inverse problems. These penalty functionals are crucial to force the regularized solution to conform to some notion of simplicity/low complexity. Classical priors of this kind includes sparsity, piecewise regularity and low-rank. These are natural assumptions for many applications, ranging from medical imaging to machine learning.
imaging - image processing - sparsity - convex optimization - inverse problem - super-resolution

Codes MSC :
47N10 - Applications in optimization, convex analysis, mathematical programming, economics
62H35 - Image analysis (statistics)
65D18 - Computer graphics, image analysis, and computational geometry
68U10 - Image processing (computing aspects)
90C31 - Sensitivity, stability, parametric optimization
94A08 - Image processing (compression, reconstruction, etc.)
80M50 - Optimization

    Informations sur la Vidéo

    Langue : Anglais
    Date de publication : 04/02/14
    Date de captation : 17/12/13
    Collection : Research talks ; Analysis and its Applications ; Mathematics in Science and Technology
    Format : QuickTime (.mov) Durée : 01:13:43
    Domaine : Analysis and its Applications ; Mathematics in Science & Technology
    Audience : Chercheurs ; Doctorants , Post - Doctorants
    Download : https://videos.cirm-math.fr/2013-12-17_Peyre.mp4

Informations sur la rencontre

Nom de la rencontre : Computational geometry days / Journées de géométrie algorithmique
Organisateurs de la rencontre : Cohen-Steiner, David ; Mérigot, Quentin
Dates : 16/12/13 - 20/12/13
Année de la rencontre : 2013

Citation Data

DOI : 10.24350/CIRM.V.18448203
Cite this video as: Peyré, Gabriel (2013). Low complexity regularization of inverse problem - Recovery guarantees. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18448203
URI : http://dx.doi.org/10.24350/CIRM.V.18448203


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