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38

CORR
2011
Springer

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How well can we estimate a sparse vector?

13 years 6 months ago

How well can we estimate a sparse vector?

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The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the sensing/design matrix being used and regardless of the estimation procedure. This lower bound very nearly matches the known upper bound one gets by taking a random projection of the sparse vector followed by an 1 estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved.

Emmanuel J. Candès, Mark A. Davenport

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Added	13 May 2011
Updated	13 May 2011
Type	Journal
Year	2011
Where	CORR
Authors	Emmanuel J. Candès, Mark A. Davenport

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