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Abstract and Applied Analysis
Volume 2014, Article ID 410104, 6 pages
http://dx.doi.org/10.1155/2014/410104
Research Article

Nonmonotone Adaptive Barzilai-Borwein Gradient Algorithm for Compressed Sensing

1School of Foreign Languages, Gannan Normal University, Ganzhou 341000, China
2School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou 341000, China
3Department of Radiology, The First Affiliated Hospital of Gannan Medical University, Ganzhou 341000, China

Received 24 January 2014; Accepted 17 March 2014; Published 7 April 2014

Academic Editor: Gaohang Yu

Copyright © 2014 Yuanying Qiu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study a nonmonotone adaptive Barzilai-Borwein gradient algorithm for -norm minimization problems arising from compressed sensing. At each iteration, the generated search direction enjoys descent property and can be easily derived by minimizing a local approximal quadratic model and simultaneously taking the favorable structure of the -norm. Under some suitable conditions, its global convergence result could be established. Numerical results illustrate that the proposed method is promising and competitive with the existing algorithms NBBL1 and TwIST.