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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 842017, 17 pages
Research Article

Backtracking-Based Simultaneous Orthogonal Matching Pursuit for Sparse Unmixing of Hyperspectral Data

1College of Astronautics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
2State Key Laboratory of Integrated Service Networks, Xidian University, Xi’an 710071, China

Received 12 November 2014; Revised 3 April 2015; Accepted 3 April 2015

Academic Editor: Kishin Sadarangani

Copyright © 2015 Fanqiang Kong 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.


Sparse unmixing is a promising approach in a semisupervised fashion by assuming that the observed signatures of a hyperspectral image can be expressed in the form of linear combination of only a few spectral signatures (endmembers) in an available spectral library. Simultaneous orthogonal matching pursuit (SOMP) algorithm is a typical simultaneous greedy algorithm for sparse unmixing, which involves finding the optimal subset of signatures for the observed data from a spectral library. But the numbers of endmembers selected by SOMP are still larger than the actual number, and the nonexisting endmembers will have a negative effect on the estimation of the abundances corresponding to the actual endmembers. This paper presents a variant of SOMP, termed backtracking-based SOMP (BSOMP), for sparse unmixing of hyperspectral data. As an extension of SOMP, BSOMP incorporates a backtracking technique to detect the previous chosen endmembers’ reliability and then deletes the unreliable endmembers. Through this modification, BSOMP can select the true endmembers more accurately than SOMP. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed algorithm.