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Séminaires IRIT-UPS


Structure-adaptive signal denoising

Dmitrii OSTROVSKII - Université Grenoble Alpes (France)

Mardi 23 Mai 2017, 10h30 - 12h00
INP-ENSEEIHT, Salle des thèses
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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 simply assume the existence of a well-performing linear estimator -- a linear oracle. Proposed estimators are able to adapt to the unknown structure of the signal, performing essentially as good as the oracle. Moreover, they can be efficiently computed through first-order convex optimization methods. Finally, we present several numerical illustrations that show the potential of the approach.

Short bio: Dmitrii Ostrovskii obtained his BSc degree in Applied Mathematics and Physics (2012) and MSc in Computer Science (2014) from the Moscow Insitute of Physics and Technology (MIPT). He is currently a 3rd year PhD student at Univ. Grenoble Alpes, advised by Anatoli Juditsky and Zaid Harchaoui (University of Washington), working on the problems in the intersection of statistical learning, optimization, and signal processing.