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.
Cite
@article{arxiv.1607.05712,
title = {Structure-Blind Signal Recovery},
author = {Dmitry Ostrovsky and Zaid Harchaoui and Anatoli Juditsky and Arkadi Nemirovski},
journal= {arXiv preprint arXiv:1607.05712},
year = {2017}
}