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Journal of Applied Mathematics
Volume 2013, Article ID 864132, 8 pages
Research Article

Tree-Based Backtracking Orthogonal Matching Pursuit for Sparse Signal Reconstruction

1School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China
2Department of Mathematics, Beijing University of Chemical Technology, Beijing 100029, China
3School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China
4Polytechnic College, Guizhou Minzu University, Guiyang, Guizhou 550025, China

Received 17 July 2013; Accepted 5 September 2013

Academic Editor: Dewei Li

Copyright © 2013 Yigang Cen 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.


Compressed sensing (CS) is a theory which exploits the sparsity characteristic of the original signal in signal sampling and coding. By solving an optimization problem, the original sparse signal can be reconstructed accurately. In this paper, a new Tree-based Backtracking Orthogonal Matching Pursuit (TBOMP) algorithm is presented with the idea of the tree model in wavelet domain. The algorithm can convert the wavelet tree structure to the corresponding relations of candidate atoms without any prior information of signal sparsity. Thus, the atom selection process will be more structural and the search space can be narrowed. Moreover, according to the backtracking process, the previous chosen atoms’ reliability can be detected and the unreliable atoms can be deleted at each iteration, which leads to an accurate reconstruction of the signal ultimately. Compared with other compressed sensing algorithms, simulation results show the proposed algorithm’s superior performance to that of several other OMP-type algorithms.