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Applied Optics

Applied Optics


  • Vol. 43, Iss. 36 — Dec. 20, 2004
  • pp: 6596–6608

Stochastic spectral unmixing with enhanced endmember class separation

Michael T. Eismann and Russell C. Hardie  »View Author Affiliations

Applied Optics, Vol. 43, Issue 36, pp. 6596-6608 (2004)

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Improvements to an algorithm for performing spectral unmixing of hyperspectral imagery based on the stochastic mixing model (SMM) are presented. The SMM provides a method for characterizing both subpixel mixing of the pure image constituents, or endmembers, and statistical variation in the endmember spectra that is due, for example, to sensor noise and natural variability of the pure constituents. Modifications of the iterative, expectation maximization approach to deriving the SMM parameter estimates are proposed, and their effects on unmixing performance are characterized. These modifications specifically concern algorithm initialization, random class assignment, and mixture constraints. The results show that the enhanced stochastic mixing model provides a better statistical representation of hyperspectral imagery from the perspective of achieving greater endmember class separation.

© 2004 Optical Society of America

OCIS Codes
(100.2000) Image processing : Digital image processing
(100.5010) Image processing : Pattern recognition

Original Manuscript: April 29, 2004
Revised Manuscript: September 20, 2004
Manuscript Accepted: September 20, 2004
Published: December 20, 2004

Michael T. Eismann and Russell C. Hardie, "Stochastic spectral unmixing with enhanced endmember class separation," Appl. Opt. 43, 6596-6608 (2004)

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  1. N. Keshava, J. F. Mustard, “Spectral unmixing,” IEEE Signal Process. Mag. 19, 44–57 (2002). [CrossRef]
  2. R. C. Hardie, M. T. Eismann, “MAP estimation for hyperspectral image resolution enhancement using an auxiliary sensor,” IEEE Trans. Image Process. 13, 1174–1184 (2004). [CrossRef] [PubMed]
  3. R. L. Sundberg, J. H. Gruninger, R. Haren, “Extraction of hyperspectral scene statistics and scene realization,” in Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VIII, S. S. Shen, P. E. Lewis, eds., Proc. SPIE4725, 184–194 (2002). [CrossRef]
  4. K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed. (Academic, San Diego, Calif., 1990), Chap. 11.
  5. A. D. Stocker, A. P. Schaum, “Application of stochastic mixing models to hyperspectral detection problems,” in Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery III, A. E. Iverson, S. S. Shen, eds., Proc. SPIE3071, 47–60 (1997).
  6. R. A. Redner, H. F. Walker, “Mixture densities, maximum likelihood, and the EM algorithm,” SIAM Rev. 26, 195–239 (1984). [CrossRef]
  7. D. W. Stein, “Stochastic compositional models applied to subpixel analysis of hyperspectral imagery,” in Imaging Spectrometry VII, M. R. Descour, S. S. Shen, eds., Proc. SPIE4480, 49–56 (2002). [CrossRef]
  8. P. Masson, W. Pieczynski, “SEM algorithm and unsupervised statistical segmentation of satellite images,” IEEE Trans. Geosci. Remote Sens. 31, 618–633 (1993). [CrossRef]
  9. R. A. Schowengerdt, Remote Sensing: Models and Methods for Image Processing, 2nd ed. (Academic, San Diego, Calif., 1997).
  10. M. E. Winter, “Fast autonomous endmember determination in hyperspectral data,” in Proceedings of the 13th International Conference on Applied Geological Remote Sensing (Environmental Research Institute of Michigan, Ann Arbor, Mich., 1999), Vol. II, pp. 337–344.
  11. H. Stark, J. W. Woods, Probability and Random Processes with Applications to Signal Processing (Prentice-Hall, Upper Saddle River, N.J., 2002), pp. 28–30.
  12. Ref. 4, p. 446.
  13. J. T. Tou, R. C. Gonzalez, Pattern Recognition Principles (Addison-Wesley, Reading, Mass., 1974), p. 87.
  14. J. R. Schott, R. Raqueno, C. Salvaggio, “Incorporation of time-dependent thermodynamic model and radiation propagation model into infrared three-dimensional synthetic image generation,” Opt. Eng. 31, 1505–1516 (1992). [CrossRef]
  15. C. Simi, J. Parish, E. M. Winter, R. Dixon, C. LaSota, M. M. Williams, “Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms,” in Algorithms for Multispectral, Hyperspectral, and Ultraspectral Imagery VI, S. S. Shen, M. R. Descour, eds., Proc. SPIE4049, 218–229 (2000). [CrossRef]
  16. J. Pearlman, S. Carman, C. Segal, P. Jarecke, P. Clancy, W. Browne, “Overview of the Hyperion imaging spectrometer for the NASA EO-1 mission,” in Proceedings of the 2002 International Geoscience and Remote Sensing Symposium (IEEE, New York, 2002), pp. 3036–3038.
  17. J. A. Hackwell, D. W. Warren, R. P. Bongiovi, S. J. Hansel, T. L. Hayhurst, D. J. Mabry, M. G. Sivjee, J. W. Skinner, “LWIR/MWIR imaging hyperspectral sensor for airborne and ground-based remote sensing,” in Imaging Spectrometry II, M. R. Descour, J. M. Mooney, eds., Proc. SPIE2819, 102–107 (1996). [CrossRef]
  18. P. G. Lucey, T. Williams, M. Mignard, J. Julian, D. Kokobun, G. Allen, D. Hampton, W. Schaff, M. Schlangen, E. M. Winter, A. Stocker, K. Horton, A. P. Bowman, “AHI: an airborne long wave infrared hyperspectral imager,” in Airborne Reconnaissance XXII, W. G. Fishell, A. A. Andraitis, M. S. Fagan, J. D. Greer, M. C. Norton, eds., Proc. SPIE3431, 36–43 (1998). [CrossRef]
  19. M. T. Eismann, R. C. Hardie, “Application of the stochastic mixing model to hyperspectral resolution enhancement,” IEEE Trans. Geosci. Remote Sens. 42, 1924–1933 (2004). [CrossRef]
  20. M. T. Eismann, R. C. Hardie, “Hyperspectral resolution enhancement using high resolution multispectral imagery with arbitrary response functions,” IEEE Trans. Geosci. Remote Sens. (to be published).

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