Lower Bounds for Sparse Recovery
Data Structures and Algorithms
2011-06-06 v2 Information Theory
math.IT
Abstract
We consider the following k-sparse recovery problem: design an m x n matrix A, such that for any signal x, given Ax we can efficiently recover x' satisfying ||x-x'||_1 <= C min_{k-sparse} x"} ||x-x"||_1. It is known that there exist matrices A with this property that have only O(k log (n/k)) rows. In this paper we show that this bound is tight. Our bound holds even for the more general /randomized/ version of the problem, where A is a random variable and the recovery algorithm is required to work for any fixed x with constant probability (over A).
Cite
@article{arxiv.1106.0365,
title = {Lower Bounds for Sparse Recovery},
author = {Khanh Do Ba and Piotr Indyk and Eric Price and David P. Woodruff},
journal= {arXiv preprint arXiv:1106.0365},
year = {2011}
}
Comments
11 pages. Appeared at SODA 2010