An Interior-Point Method for Large-Scale l1-Regularized Least Squares
Seung-Jean Kim
Koh, K.
Lustig, M.
Boyd, S.
Gorinevsky, D.
Stanford Univ., Stanford;
This paper appears in: Selected Topics in Signal Processing, IEEE Journal of
Publication Date: Dec. 2007
Volume: 1,
Issue: 4
On page(s): 606-617
ISSN: 1932-4553
INSPEC Accession Number: 9742908
Digital Object Identifier: 10.1109/JSTSP.2007.910971
Current Version Published: 2008-01-07
Abstract
Recently, a lot of attention has been paid to 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 -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 -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.
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