Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds
Abstract
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the measurement rate and per-sample signal-to-noise ratio (SNR) are finite constants independent of the length of the vector, then the optimal sparsity pattern estimate will have a constant fraction of errors. Lower bounds on the measurement rate needed to attain a desired fraction of errors are given in terms of the SNR and various key parameters of the unknown vector. The tightness of the bounds in a scaling sense, as a function of the SNR and the fraction of errors, is established by comparison with existing achievable bounds. Near optimality is shown for a wide variety of practically motivated signal models.
Cite
@article{arxiv.1002.4458,
title = {Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds},
author = {Galen Reeves and Michael Gastpar},
journal= {arXiv preprint arXiv:1002.4458},
year = {2013}
}