This is an announcement for the paper "Reconstruction from anisotropic random measurements" by Mark Rudelson and Shuheng Zhou.

Abstract: Random matrices are widely used in sparse recovery problems, and the relevant properties of matrices with i.i.d. entries are well understood. The current paper discusses the recently introduced Restricted Eigenvalue (RE) condition, which is among the most general assumptions on the matrix, guaranteeing recovery. We prove a reduction principle showing that the RE condition can be guaranteed by checking the restricted isometry on a certain family of low-dimensional subspaces. This principle allows us to establish the RE condition for several broad classes of random matrices with dependent entries, including random matrices with subgaussian rows and non-trivial covariance structure, as well as matrices with independent rows, and uniformly bounded entries.

Archive classification: math.ST cs.IT math.FA math.IT stat.TH

Report Number: Technical Report 522, University of Michigan, Department of Statistics

Remarks: 30 Pages

Submitted from: szhou@cs.cmu.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1106.1151

or

http://arXiv.org/abs/1106.1151