Tight Sufficient Conditions on Exact Sparsity Pattern Recovery
Information Theory
2014-06-26 v3 math.IT
Abstract
A noisy underdetermined system of linear equations is considered in which a sparse vector (a vector with a few nonzero elements) is subject to measurement. The measurement matrix elements are drawn from a Gaussian distribution. We study the information-theoretic constraints on exact support recovery of a sparse vector from the measurement vector and matrix. We compute a tight, sufficient condition that is applied to ergodic wide-sense stationary sparse vectors. We compare our results with the existing bounds and recovery conditions. Finally, we extend our results to approximately sparse signals.
Cite
@article{arxiv.1209.4209,
title = {Tight Sufficient Conditions on Exact Sparsity Pattern Recovery},
author = {Behrooz Kamary Aliabadi and Silèye Ba},
journal= {arXiv preprint arXiv:1209.4209},
year = {2014}
}