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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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Submitted on : Monday, July 18, 2016 - 5:15:05 AM
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Dmitry Ostrovsky, Zaid Harchaoui, Anatoli B. Juditsky, Arkadi Nemirovski. Structure-Blind Signal Recovery. 30th International Conference on Neural Information Processing Systems - NIPS'16, Dec 2016, Barcelona, Spain. pp.4824-4832. ⟨hal-01345960⟩

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