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arXiv · 1607.05712

Structure-Blind Signal Recovery

Dmitry Ostrovsky·Zaid Harchaoui·Anatoli Juditsky·Arkadi Nemirovski
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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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Dmitry Ostrovsky, Zaid Harchaoui, Anatoli Juditsky, Arkadi Nemirovski. 2016-07-19. Structure-Blind Signal Recovery. https://arxiv.org/abs/1607.05712

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