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Mathematical Problems in Engineering
Volume 2013, Article ID 498589, 6 pages
Research Article

Sparse Recovery by Semi-Iterative Hard Thresholding Algorithm

1School of Science, Xidian University, Xi’an, Shaanxi 710071, China
2School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
3School of Statistics, Xi’an University of Finance and Economics, Xi’an, Shaanxi 710100, China

Received 7 October 2012; Revised 30 November 2012; Accepted 10 December 2012

Academic Editor: Ion Zaballa

Copyright © 2013 Xueqin Zhou 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.


We propose a computationally simple and efficient method for sparse recovery termed as the semi-iterative hard thresholding (SIHT). Unlike the existing iterative-shrinkage algorithms, which rely crucially on using negative gradient as the search direction, the proposed algorithm uses the linear combination of the current gradient and directions of few previous steps as the search direction. Compared to other iterative shrinkage algorithms, the performances of the proposed method show a clear improvement in iterations and error in noiseless, whilst the computational complexity does not increase.