By Topic

Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Gongguo Tang ; Preston M. Green Dept. of Electr. & Syst. Eng., Washington Univ. in St. Louis, St. Louis, MO, USA ; Nehorai, Arye

The stability of sparse signal reconstruction with respect to measurement noise is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique 1 sparse recovery. One of our algorithms produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the 1 -constrained minimal singular value (1-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of 1-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared to performance analysis involving the Restricted Isometry Constant, the arguments in this paper are much less complicated and provide more intuition on the stability of sparse signal recovery. We show also that, with high probability, the subgaussian ensemble generates measurement matrices with 1-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the 1-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semidefinite relaxation.

Published in:

Signal Processing, IEEE Transactions on  (Volume:59 ,  Issue: 12 )