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Adaptive Recovery of Signals by Convex Optimization

Zaid Harchaoui 1, 2 Anatoli B. Juditsky 3 Arkadi Nemirovski 4, * Dmitry Ostrovsky 3 
* Corresponding author
2 LEAR - Learning and recognition in vision
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
3 SAM - Statistique Apprentissage Machine
LJK - Laboratoire Jean Kuntzmann
Abstract : We present a theoretical framework for adaptive estimation and prediction of signals of unknown structure in the presence of noise. The framework allows to address two intertwined challenges: (i) designing optimal statistical estimators; (ii) designing efficient numerical algorithms. In particular, we establish oracle inequalities for the performance of adaptive procedures, which rely upon convex optimization and thus can be efficiently implemented. As an application of the proposed approach, we consider denoising of harmonic oscillations.
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Submitted on : Monday, January 4, 2016 - 2:41:55 PM
Last modification on : Friday, November 18, 2022 - 9:28:19 AM
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  • HAL Id : hal-01250215, version 1


Zaid Harchaoui, Anatoli B. Juditsky, Arkadi Nemirovski, Dmitry Ostrovsky. Adaptive Recovery of Signals by Convex Optimization. JMLR Workshop and Conference Proceedings, Jul 2015, Paris, France. pp.929-955. ⟨hal-01250215⟩



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