Journal
IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
Volume 1, Issue 4, Pages 606-617Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/JSTSP.2007.910971
Keywords
Basis pursuit denoising; compressive sampling; compressed sensing; convex optimization; interior-point methods; least squares; preconditioned conjugate gradients; l(1) regularization
Categories
Funding
- Focus Center Research Program Center for Circuit and System Solutions [2003-CT-888]
- JPL [1291856]
- Precourt Institute on Energy Efficiency
- Army award [W911NF-07-1-0029]
- NSF [ECS-0423905, 0529426]
- DARPA [FA9550-06-1-0514]
- AFOSR [FA9550-06-1-0312]
Ask authors/readers for more resources
Recently, a lot of attention has been paid to l(1) regularization based methods for sparse signal reconstruction (e.g., basis pursuit denoising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l(1)-regularized least-squares programs (LSPs), which can be reformulated as convex quadratic programs, and then solved by several standard methods such as interior-point methods, at least for small and medium size problems. In this paper, we describe a specialized interior-point method for solving large-scale, l(1)-regularized LSPs that uses the preconditioned conjugate gradients algorithm to compute the search direction. The interior-point method can solve large sparse problems, with a million variables and observations, in a few tens of minutes on a PC. It can efficiently solve large dense problems, that arise in sparse signal recovery with orthogonal transforms, by exploiting fast algorithms for these transforms. The method is illustrated on a magnetic resonance imaging data set.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available