Computable performance guarantees for compressed sensing matrices

Type
Article

Authors
Cho, Myung
Vijay Mishra, Kumar
Xu, Weiyu

KAUST Grant Number
OCRF-2014-CRG-3

Online Publication Date
2018-02-27

Print Publication Date
2018-12

Date
2018-02-27

Abstract
The null space condition for ℓ1 minimization in compressed sensing is a necessary and sufficient condition on the sensing matrices under which a sparse signal can be uniquely recovered from the observation data via ℓ1 minimization. However, verifying the null space condition is known to be computationally challenging. Most of the existing methods can provide only upper and lower bounds on the proportion parameter that characterizes the null space condition. In this paper, we propose new polynomial-time algorithms to establish upper bounds of the proportion parameter. We leverage on these techniques to find upper bounds and further develop a new procedure—tree search algorithm—that is able to precisely and quickly verify the null space condition. Numerical experiments show that the execution speed and accuracy of the results obtained from our methods far exceed those of the previous methods which rely on linear programming (LP) relaxation and semidefinite programming (SDP).

Citation
Cho M, Vijay Mishra K, Xu W (2018) Computable performance guarantees for compressed sensing matrices. EURASIP Journal on Advances in Signal Processing 2018. Available: http://dx.doi.org/10.1186/s13634-018-0535-y.

Acknowledgements
The work of Weiyu Xu is supported by Simons Foundation 318608, KAUST OCRF-2014-CRG-3, NSF DMS-1418737, and NIH 1R01EB020665-01.

Publisher
Springer Nature

Journal
EURASIP Journal on Advances in Signal Processing

DOI
10.1186/s13634-018-0535-y

Permanent link to this record
http://hdl.handle.net/10754/629746
Collections
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