Structure-Blind Signal Recovery
Dmitry Ostrovsky, Zaid Harchaoui, Anatoli Juditsky, Arkadi S. Nemirovski
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.
BibTeX
@inproceedings{NIPS2016_2f4fe03d,
author = {Ostrovsky, Dmitry and Harchaoui, Zaid and Juditsky, Anatoli and Nemirovski, Arkadi S},
booktitle = {Advances in Neural Information Processing Systems},
editor = {D. Lee and M. Sugiyama and U. Luxburg and I. Guyon and R. Garnett},
pages = {},
publisher = {Curran Associates, Inc.},
title = {Structure-Blind Signal Recovery},
url = {https://proceedings.neurips.cc/paper_files/paper/2016/file/2f4fe03d77724a7217006e5d16728874-Paper.pdf},
volume = {29},
year = {2016}
}