Primal and dual alternating direction algorithms for ℓ 1 -ℓ 1 -norm minimization problems in compressive sensing

Yunhai Xiao (), Hong Zhu () and Soon-Yi Wu ()

Computational Optimization and Applications, 2013, vol. 54, issue 2, 459 pages

Abstract: In this paper, we propose, analyze and test primal and dual versions of the alternating direction algorithm for the sparse signal reconstruction from its major noise contained observation data. The algorithm minimizes a convex non-smooth function consisting of the sum of ℓ 1 -norm regularization term and ℓ 1 -norm data fidelity term. We minimize the corresponding augmented Lagrangian function alternatively from either primal or dual forms. Both of the resulting subproblems admit explicit solutions either by using a one-dimensional shrinkage or by an efficient Euclidean projection. The algorithm is easily implementable and it requires only two matrix-vector multiplications per-iteration. The global convergence of the proposed algorithm is established under some technical conditions. The extensions to the non-negative signal recovery problem and the weighted regularization minimization problem are also discussed and tested. Numerical results illustrate that the proposed algorithm performs better than the state-of-the-art algorithm YALL1. Copyright Springer Science+Business Media, LLC 2013

Keywords: Compressive sensing; Sparse optimization; Alternating direction method; Dual problem; Augmented Lagrangian function (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1007/s10589-012-9475-x (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:54:y:2013:i:2:p:441-459

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-012-9475-x

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().