How well can we estimate a sparse vector?

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.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Emmanuel J. Candès, Mark A. Davenport
• Keywords: Compressive Sensing, CORR 2011, Education, Estimation Procedure, Sparse Vector