Joint sparsity with different measurement matrices

Authors

Reinhard Heckel and Helmut Bölcskei

Reference

Allerton Conference on Communication, Control, and Computing, Monticello, IL, pp. 698-702, Oct. 2012, (invited paper)

DOI: 10.1109/Allerton.2012.6483286

[BibTeX, LaTeX, and HTML Reference]

Abstract

We consider a generalization of the multiple measurement vector (MMV) problem, where the measurement matrices are allowed to differ across measurements. This problem arises naturally when multiple measurements are taken over time, e.g., and the measurement modality (matrix) is time-varying. We derive probabilistic recovery guarantees showing that---under certain (mild) conditions on the measurement matrices---l2/l1-norm minimization and a variant of orthogonal matching pursuit fail with a probability that decays exponentially in the number of measurements. This allows us to conclude that, perhaps surprisingly, recovery performance does not suffer from the individual measurements being taken through different measurement matrices. What is more, recovery performance typically benefits (significantly) from diversity in the measurement matrices; we specify conditions under which such improvements are obtained. These results continue to hold when the measurements are subject to (bounded) noise.


Download this document:

 

Copyright Notice: © 2012 R. Heckel and H. Bölcskei.

This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.