How well can we estimate a sparse vector?
Information Theory
2013-03-04 v5 math.IT
Statistics Theory
Statistics Theory
Abstract
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix being used and regardless of the estimation procedure. This lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved.
Cite
@article{arxiv.1104.5246,
title = {How well can we estimate a sparse vector?},
author = {Emmanuel J. Candès and Mark A. Davenport},
journal= {arXiv preprint arXiv:1104.5246},
year = {2013}
}