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Poster
Structure-Blind Signal Recovery
Dmitry Ostrovsky · Zaid Harchaoui · Anatoli Juditsky · Arkadi S Nemirovski

Wed Dec 07 09:00 AM -- 12:30 PM (PST) @ Area 5+6+7+8 #47
in Wednesday Posters »

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.

Keywords: Learning Theory · (Application) Signal and Speech Processing
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Author Information

Dmitry Ostrovsky (Univ. Grenoble Alpes)
Zaid Harchaoui (NYU)
Anatoli Juditsky (UJF)
Arkadi S Nemirovski (Gerogia Institute of Technology)

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