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.
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Pré-publication, Document de travail
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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



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



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