Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published 2012 | public
Book Section - Chapter

Deterministic phase guarantees for robust recovery in incoherent dictionaries

Abstract

This paper presents a relaxation of an assumption usually imposed in the recovery of sparse vectors with random support in pairs of orthonormal bases or incoherent dictionaries by basis pursuit. The assumption requires the phases of the entries of the sparse vector to be chosen randomly in [0, 2π). This paper provides probabilistic recovery guarantees for deterministic phases. We prove that, if a phase pattern is fixed, then a sparse vector with random support and corresponding phases can be recovered with high probability. As a result, the phases can take any distribution and can be dependent, as long as they are independent of the support. Furthermore, this improvement does not come at the expense of the maximum recoverable sparsity.

Additional Information

© 2012 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927., by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech's Lee Center for Advanced Networking. This work was performed while the first author was an exchange student at the California Institute of Technology, supported by Professor Charles K. Kao Research Exchange Scholarship of The Chinese University of Hong Kong.

Additional details

Created:
August 19, 2023
Modified:
March 5, 2024