Fast implementation of kernel simplex volume analysis based on modified Cholesky factorization for endmember extraction

  • Jing Li
  • Xiao-run Li
  • Li-jiao Wang
  • Liao-ying Zhao
Article

Abstract

Endmember extraction is a key step in the hyperspectral image analysis process. The kernel new simplex growing algorithm (KNSGA), recently developed as a nonlinear alternative to the simplex growing algorithm (SGA), has proven a promising endmember extraction technique. However, KNSGA still suffers from two issues limiting its application. First, its random initialization leads to inconsistency in final results; second, excessive computation is caused by the iterations of a simplex volume calculation. To solve the first issue, the spatial pixel purity index (SPPI) method is used in this study to extract the first endmember, eliminating the initialization dependence. A novel approach tackles the second issue by initially using a modified Cholesky factorization to decompose the volume matrix into triangular matrices, in order to avoid directly computing the determinant tautologically in the simplex volume formula. Theoretical analysis and experiments on both simulated and real spectral data demonstrate that the proposed algorithm significantly reduces computational complexity, and runs faster than the original algorithm.

Key words

Endmember extraction Modified Cholesky factorization Spatial pixel purity index (SPPI) New simplex growing algorithm (NSGA) Kernel new simplex growing algorithm (KNSGA) 

CLC number

TP75 

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References

  1. Boardman, J.W., Kruse, F.A., Green, R.O., 1995. Mapping target signatures via partial unmixing of AVIRIS data. JPL Airborne Earth Science Workshop, p.23–26.Google Scholar
  2. Chang, C.I., Du, Q., 2004. Estimation of number of spectrally distinct signal sources in hyperspectral imagery. IEEE Trans. Geosci. Remote Sens., 42(3):608–619. http://dx.doi.org/10.1109/TGRS.2003.819189CrossRefGoogle Scholar
  3. Chang, C.I., Wu, C., Liu, W., et al., 2006. A new growing method for simplex-based endmember extraction algorithms. IEEE Trans. Geosci. Remote Sens., 44(10):2804–2819. http://dx.doi.org/10.1109/TGRS.2006.881803CrossRefGoogle Scholar
  4. Cui, J.T., Wang, J., Li, X.R., et al., 2013. Endmember extraction algorithm based on spatial pixel purity index. J. Zhejiang Univ. (Eng. Sci.), 47(9):1517–1523 (in Chinese). http://dx.doi.org/10.3785/j.issn.1008-973X.2013.09.002Google Scholar
  5. Dowler, S.W., Takashima, R., Andrews, M., 2013. Reducing the complexity of the N-FINDR algorithm for hyperspectral image analysis. IEEE Trans. Image Process., 22(7):2835–2848. http://dx.doi.org/10.1109/TIP.2012.2219546CrossRefGoogle Scholar
  6. Geng, X.R., Zhao, Y.C., Wang, F.X., et al., 2010. A new volume formula for a simplex and its application to endmember extraction for hyperspectral image analysis. Int. J. Remote Sens., 31(4):1027–1035. http://dx.doi.org/10.1080/01431160903154283CrossRefGoogle Scholar
  7. Geng, X.R., Xiao, Z.Q., Ji, L.Y., et al., 2013. A Gaussian elimination based fast endmember extraction algorithm for hyperspectral imagery. ISPRS J. Photogr. Remote Sens., 79(5):211–218. http://dx.doi.org/10.1016/j.isprsjprs.2013.02.020CrossRefGoogle Scholar
  8. Gill, P.E., Murray, W., 1974. Newton-type method for unconstrained and linearly constrained optimization. Math. Programm., 7(1):311–350. http://dx.doi.org/10.1007/BF01585529MathSciNetCrossRefMATHGoogle Scholar
  9. Gill, P.E., Murray, W., Wright, M.H., 1981. Practical Optimization. Academic Press, London.MATHGoogle Scholar
  10. Golub, G.H., van Loan, C.F., 1996. Matrix Computations. The John Hopkins University Press, Baltimore, Mariland.MATHGoogle Scholar
  11. Liu, J.M., Zhang, J.S., 2012. A new maximum simplex volume method based on householder transformation for endmember extraction. IEEE Trans. Geosci. Remote Sens., 50(1):104–118. http://dx.doi.org/10.1109/TGRS.2011.2158829CrossRefGoogle Scholar
  12. Miao, L., Qi, H., 2007. Endmember extraction from highly mixed data using minimum volume constrained nonnegative matrix factorization. IEEE Trans. Geosci. Remote Sens., 45(3):765–777. http://dx.doi.org/10.1109/TGRS.2006.888466CrossRefGoogle Scholar
  13. NASA, 1997. NASA AVIRIS Data. Available from http://aviris.jpl.nasa.gov.Google Scholar
  14. Nascimento, J.M.P., Bioucas-Dias, J.M., 2005. Vertex component analysis: a fast algorithm to unmix hyperspectral data. IEEE Trans. Geosci. Remote Sens., 43(4):898–910. http://dx.doi.org/10.1109/TGRS.2005.844293CrossRefGoogle Scholar
  15. Nascimento, J.M.P., Bioucas-Dias, J.M., 2008. New developments on VCA unmixing algorithm. SPIE, 7109: 71090F. http://dx.doi.org/10.1117/12.799838Google Scholar
  16. Ren, H., Chang, C.I., 2003. Automatic spectral target recognition in hyperspectral imagery. IEEE Trans. Aerosp. Electron. Syst., 39(4):1232–1249. http://dx.doi.org/10.1109/TAES.2003.1261124CrossRefGoogle Scholar
  17. Schowengerdt, R.A., 1997. Remote Sensing: Models and Methods for Image Processing. Academic Press, New York.Google Scholar
  18. Sun, K., Geng, X., Wang, P., 2014. A fast endmember extraction algorithm based on gram determinant. IEEE Geosci. Remote Sens. Lett., 11(6):1124–1128. http://dx.doi.org/10.1109/LGRS.2013.2288093CrossRefGoogle Scholar
  19. Tao, X., Wang, B., Zhang, L., 2009. Orthogonal bases approach for decomposition of mixed pixels for hyperspectral imagery. IEEE Geosci. Remote Sens. Lett., 6(2):219–223. http://dx.doi.org/10.1109/LGRS.2008.2010529CrossRefMATHGoogle Scholar
  20. Wang, L., Wei, F., Liu, D., 2013. Fast implementation of maximum simplex volume-based endmember extraction in original hyperspectral data space. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 6(2):516–521. http://dx.doi.org/10.1109/JSTARS.2012.2234439MathSciNetCrossRefGoogle Scholar
  21. Wang, L.J., Li, X.R., Zhao, L.Y., 2014. Fast implement of the simplex growing algorithm for endmember extraction. Acta Opt. Sin., 34(11):1128001 (in Chinese). http://dx.doi.org/10.3788/AOS201434.1128001CrossRefGoogle Scholar
  22. Xia, W., Pu, H.Y., Wang, B., et al., 2012. Triangular factorization-based simplex algorithms for hyperspectral unmixing. IEEE Trans. Geosci. Remote Sens., 50(11):4420–4440. http://dx.doi.org/10.1109/TGRS.2012.2195185CrossRefGoogle Scholar
  23. Xiong, W., Chang, C.I., Wu, C.C., 2011. Fast algorithms to implement N-FINDR for hyperspectral endmember extraction. IEEE J. Sel. Topics Appl. Earth Observ. Remote Sens., 4(3):545–564. http://dx.doi.org/10.1109/JSTARS.2011.2119466CrossRefGoogle Scholar
  24. Zhao, C.H., Qi, B., Wang, Y.L., 2012. An improved N-FINDR hyperspectral endmember extraction algorithm. J. Electron. Inform. Technol., 34(2):499–503 (in Chinese).Google Scholar
  25. Zhao, L.Y., Zheng, J.P., Li, X.R., et al., 2014. Kernel simplex growing algorithm based on a new simplex volume formula for hyperspectral endmember extraction. J. Appl. Remote Sens., 8(1):083594. http://dx.doi.org/10.1117/1.JRS.8.083594CrossRefGoogle Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Jing Li
    • 1
  • Xiao-run Li
    • 1
  • Li-jiao Wang
    • 1
  • Liao-ying Zhao
    • 2
  1. 1.College of Electrical EngineeringZhejiang UniversityHangzhouChina
  2. 2.Institute of Computer Application TechnologyHangzhou Dianzi UniversityHangzhouChina

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