Structure-Blind Signal Recovery

Abstract : We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of the minimax risk. However, when the set is unspecified, designing an estimator that is blind to the hidden structure of the signal remains a challenging problem. We propose a new family of estimators to recover signals observed in Gaussian noise. Instead of specifying the set where the signal lives, we assume the existence of a well-performing linear estimator. Proposed estimators enjoy exact oracle inequalities and can be efficiently computed through convex optimization. We present several numerical illustrations that show the potential of the approach.
Type de document :
Pré-publication, Document de travail
2016
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Contributeur : Zaid Harchaoui <>
Soumis le : lundi 18 juillet 2016 - 05:15:05
Dernière modification le : lundi 30 avril 2018 - 15:02:01

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  • HAL Id : hal-01345960, version 1

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Dmitry Ostrovsky, Zaid Harchaoui, Anatoli Juditsky, Arkadi Nemirovski. Structure-Blind Signal Recovery. 2016. 〈hal-01345960〉

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