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Adaptive Recovery of Signals by Convex Optimization

Zaid Harchaoui 1, 2 Anatoli 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, INPG - Institut National Polytechnique de Grenoble
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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Zaid Harchaoui, Anatoli 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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