Lower bounds for sparse recovery
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Indyk_Lower bounds.pdf
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219.21 KB
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Author(s)
Indyk, Piotr
Do Ba, Khanh
Price, Eric C.
Woodruff, David P.
Date Issued
January 2010
Journal
Proceedings of the Twenty-First Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
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.
Version
Author's final manuscript
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 [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).
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
http://www.siam.org/proceedings/soda/2010/SODA10_095_dobak.pdf
