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Mathematical Problems in Engineering
Volume 2014, Article ID 107620, 8 pages
http://dx.doi.org/10.1155/2014/107620
Research Article

Neural Network for Sparse Reconstruction

1School of Information and Computer Engineering, Northeast Forestry University, No. 26, Hexing Street, Harbin 150040, China
2College of Electromechanical Engineering, Northeast Forestry University, No. 26, Hexing Street, Harbin 150040, China

Received 24 December 2013; Accepted 4 March 2014; Published 31 March 2014

Academic Editor: Huaiqin Wu

Copyright © 2014 Qingfa Li 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 construct a neural network based on smoothing approximation techniques and projected gradient method to solve a kind of sparse reconstruction problems. Neural network can be implemented by circuits and can be seen as an important method for solving optimization problems, especially large scale problems. Smoothing approximation is an efficient technique for solving nonsmooth optimization problems. We combine these two techniques to overcome the difficulties of the choices of the step size in discrete algorithms and the item in the set-valued map of differential inclusion. In theory, the proposed network can converge to the optimal solution set of the given problem. Furthermore, some numerical experiments show the effectiveness of the proposed network in this paper.