Computer Science – Information Theory
Scientific paper
2010-04-23
Computer Science
Information Theory
Scientific paper
The stability of sparse signal reconstruction is investigated in this paper. We design efficient algorithms to verify the sufficient condition for unique $\ell_1$ sparse recovery. One of our algorithm produces comparable results with the state-of-the-art technique and performs orders of magnitude faster. We show that the $\ell_1$-constrained minimal singular value ($\ell_1$-CMSV) of the measurement matrix determines, in a very concise manner, the recovery performance of $\ell_1$-based algorithms such as the Basis Pursuit, the Dantzig selector, and the LASSO estimator. Compared with 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 $\ell_1$-CMSVs bounded away from zero, as long as the number of measurements is relatively large. To compute the $\ell_1$-CMSV and its lower bound, we design two algorithms based on the interior point algorithm and the semi-definite relaxation.
Nehorai Arye
Tang Gongguo
No associations
LandOfFree
Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Performance Analysis of Sparse Recovery Based on Constrained Minimal Singular Values will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-386647