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Low complexity regularization of inverse problem - Recovery guarantees

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Post-edited
Authors : Peyré, Gabriel (Author of the conference)
CIRM (Publisher )

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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
Abstract : 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

MSC Codes :
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
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 04/02/14
    Conference Date : 17/12/2013
    Subseries : Research talks
    arXiv category : Statistics Theory ; Optimization and Control ; Machine Learning
    Mathematical Area(s) : Analysis and its Applications ; Mathematics in Science & Technology
    Format : QuickTime (.mov) Video Time : 01:13:43
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2013-12-17_Peyre.mp4
Information on the Event

Event Title : Computational geometry days / Journées de géométrie algorithmique
Event Organizers : Cohen-Steiner, David ; Mérigot, Quentin
Dates : 16/12/13 - 20/12/13
Event Year : 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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