Lower bounds for sparse recovery
Author(s)Indyk, Piotr; Do Ba, Khanh; Price, Eric C.; Woodruff, David P.
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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 [less than or equal to] C min[subscript 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 random- ized 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).
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
Society for Industrial and Applied Mathematics
Do Ba, Khanh et al. "Lower Bounds for Sparse Recovery." in Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms, Session 9A, Jan. 17-19, 2010, Hyatt Regency Austin, Austin, TX.
Author's final manuscript