Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605247 | Applied and Computational Harmonic Analysis | 2013 | 7 Pages |
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 â„“1 estimation procedure such as the Dantzig selector. In this sense, compressive sensing techniques cannot essentially be improved.
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