How well can we estimate a sparse vector?

Emmanuel J. Candès; Mark A. Davenport

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arXiv · 1104.5246

How well can we estimate a sparse vector?

Emmanuel J. Candès·Mark A. Davenport

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Abstract

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 $\ell_1$ estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved.

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Emmanuel J. Candès, Mark A. Davenport. 2011-04-27. How well can we estimate a sparse vector?. https://arxiv.org/abs/1104.5246

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