Abstract

Hyperspectral imaging systems for daylight operation measure and analyze reflected and scattered radiation in p-spectral channels covering the reflective infrared region 0.42.5μm. Consequently, the p-dimensional joint distribution of background clutter is required to design and evaluate optimum hyperspectral imaging processors. In this paper, we develop statistical models for the spectral variability of natural hyperspectral backgrounds using the class of elliptically contoured distributions. We demonstrate, using data from the NASA AVIRIS sensor, that models based on the multivariate t-elliptically contoured distribution capture with sufficient accuracy the statistical characteristics of natural hyperspectral backgrounds that are relevant to target detection applications.

© 2008 Optical Society of America

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  1. D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
    [CrossRef]
  2. D. Manolakis, “Realistic matched filter performance prediction for hyperspectral target detection,” Opt. Eng. 44, 116401 (2005).
    [CrossRef]
  3. J. B. Adams, M. O. Smith, and A. R. Gillespie, “Imaging spectroscopy: Interpretation based on spectral mixture analysis,” in Remote Geochemical Analysis: Elemental and Mineralogical Composition C. M. Pieters and P. A. J. Englert, eds. (Cambridge University Press, 1993), pp. 145-166.
  4. J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
    [CrossRef]
  5. Strictly speaking Δ is the Mahalanobis distance and Δ2 is the squared Mahalanobis distance; however, for simplicity, the term Mahalanobis distance is used in both cases. The exact meaning should be clear from the context.
  6. S. Kotz and S. Nadarajah, Multivariate t-Distributions and Their Applications (Cambridge University Press, 2004).
  7. T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed. (Wiley, 2003),
  8. K. T. Fang, S. Kotz, and K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1990).
  9. M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
    [CrossRef]
  10. R. Gnanadesikan, Methods for Statistical Data Analysis of Multivariate Observations, 2nd ed. (Wiley, 1997),
  11. M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
    [CrossRef]
  12. D. Marden and D. Manolakis, “Statistical modeling of hyperspectral imaging data and their applications,” Tech. Rep. HTAp-16 (Lincoln Laboratory, 2004).
  13. D. Marden and D. Manolakis, “Modeling hyperspectral imaging sata using elliptically contoured distributions,” Proc. SPIE 5093, 253-262 (2003).
    [CrossRef]
  14. R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
    [CrossRef]
  15. S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.
  16. S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
    [CrossRef]
  17. M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
    [CrossRef]
  18. N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).
  19. D. Manolakis and D. Marden, “Dimensionality reduction of hyperspectral imaging data using local principal component transforms,” Proc. SPIE 5425, 393-401 (2004).
    [CrossRef]
  20. M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
    [CrossRef]

2007 (1)

N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).

2006 (2)

M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
[CrossRef]

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

2005 (1)

D. Manolakis, “Realistic matched filter performance prediction for hyperspectral target detection,” Opt. Eng. 44, 116401 (2005).
[CrossRef]

2004 (2)

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

D. Manolakis and D. Marden, “Dimensionality reduction of hyperspectral imaging data using local principal component transforms,” Proc. SPIE 5425, 393-401 (2004).
[CrossRef]

2003 (2)

D. Marden and D. Manolakis, “Modeling hyperspectral imaging sata using elliptically contoured distributions,” Proc. SPIE 5093, 253-262 (2003).
[CrossRef]

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

2001 (1)

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

1999 (1)

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

1998 (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

1993 (1)

M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
[CrossRef]

Acharya, P.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Acharya, P. K.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Acito, N.

N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).

Adams, J. B.

J. B. Adams, M. O. Smith, and A. R. Gillespie, “Imaging spectroscopy: Interpretation based on spectral mixture analysis,” in Remote Geochemical Analysis: Elemental and Mineralogical Composition C. M. Pieters and P. A. J. Englert, eds. (Cambridge University Press, 1993), pp. 145-166.

Adler-Golden, S.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Allred, C. L.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Anderson, G.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Anderson, G. P.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Anderson, T. W.

T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed. (Wiley, 2003),

Aronsson, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Berk, A.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Bernhardt, M.

M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
[CrossRef]

Bernstein, L.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Bernstein, L. S.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Burke, K.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Chetwynd, J. H.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Chippendale, B. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Chovit, C. J.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Chrien, T. G.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Cipar, J.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

Cooley, T.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

Corsini, G.

N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).

Diani, M.

N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).

Eastwood, M. L.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Fang, K. T.

K. T. Fang, S. Kotz, and K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1990).

Faust, J. A.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Felde, G.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

Felde, J. W.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Gardner, J.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Gillespie, A. R.

J. B. Adams, M. O. Smith, and A. R. Gillespie, “Imaging spectroscopy: Interpretation based on spectral mixture analysis,” in Remote Geochemical Analysis: Elemental and Mineralogical Composition C. M. Pieters and P. A. J. Englert, eds. (Cambridge University Press, 1993), pp. 145-166.

Gnanadesikan, R.

R. Gnanadesikan, Methods for Statistical Data Analysis of Multivariate Observations, 2nd ed. (Wiley, 1997),

Golden-Adler, S.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Gorodetzky, D.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

Green, R. O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Grigsby, P.

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

Heather, J.

M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
[CrossRef]

Hoke, M.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

hua, H.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Jacobson, J.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

Jeong, L.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Jeong, L. S.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Kerekes, J.

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

Kotz, S.

S. Kotz and S. Nadarajah, Multivariate t-Distributions and Their Applications (Cambridge University Press, 2004).

K. T. Fang, S. Kotz, and K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1990).

Levine, R.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Lockwood, R.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

Manolakis, D.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

D. Manolakis, “Realistic matched filter performance prediction for hyperspectral target detection,” Opt. Eng. 44, 116401 (2005).
[CrossRef]

D. Manolakis and D. Marden, “Dimensionality reduction of hyperspectral imaging data using local principal component transforms,” Proc. SPIE 5425, 393-401 (2004).
[CrossRef]

D. Marden and D. Manolakis, “Modeling hyperspectral imaging sata using elliptically contoured distributions,” Proc. SPIE 5093, 253-262 (2003).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

D. Marden and D. Manolakis, “Statistical modeling of hyperspectral imaging data and their applications,” Tech. Rep. HTAp-16 (Lincoln Laboratory, 2004).

Marden, D.

D. Manolakis and D. Marden, “Dimensionality reduction of hyperspectral imaging data using local principal component transforms,” Proc. SPIE 5425, 393-401 (2004).
[CrossRef]

D. Marden and D. Manolakis, “Modeling hyperspectral imaging sata using elliptically contoured distributions,” Proc. SPIE 5093, 253-262 (2003).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

D. Marden and D. Manolakis, “Statistical modeling of hyperspectral imaging data and their applications,” Tech. Rep. HTAp-16 (Lincoln Laboratory, 2004).

Matthew, M.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

Matthew, M. L.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Matthew, M. W.

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Nadarajah, S.

S. Kotz and S. Nadarajah, Multivariate t-Distributions and Their Applications (Cambridge University Press, 2004).

Ng, K. W.

K. T. Fang, S. Kotz, and K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1990).

Olah, M. R.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Ozturk, A.

M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
[CrossRef]

Paswaters, S.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

Pavri, B. E.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Pukall, B.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Rangaswamy, M.

M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
[CrossRef]

Ratkowski, A.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

Richtsmeier, S.

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

Rossacci, M.

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

Sarture, C. M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Shaw, G.

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

Shippert, M.

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

Smith, M. O.

J. B. Adams, M. O. Smith, and A. R. Gillespie, “Imaging spectroscopy: Interpretation based on spectral mixture analysis,” in Remote Geochemical Analysis: Elemental and Mineralogical Composition C. M. Pieters and P. A. J. Englert, eds. (Cambridge University Press, 1993), pp. 145-166.

Solis, M.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Watkins, O.

M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
[CrossRef]

Weiner, D.

M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
[CrossRef]

Williams, O.

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

EURASIP J. Appl. Signal Process. (1)

N. Acito, G. Corsini, and M. Diani, “Statistical analysis of hyper-spectral data: A non-gaussian approach,” EURASIP J. Appl. Signal Process. 2007, 27673 (2007).

IEEE Trans. Aerosp. Electron. Syst. (1)

M. Rangaswamy, D. Weiner, and A. Ozturk, “Non-Gaussian random vector identification using spherically invariant random processes,” IEEE Trans. Aerosp. Electron. Syst. 29, 111-124 (1993).
[CrossRef]

Opt. Eng. (1)

D. Manolakis, “Realistic matched filter performance prediction for hyperspectral target detection,” Opt. Eng. 44, 116401 (2005).
[CrossRef]

Proc. SPIE (8)

J. Cipar, R. Lockwood, T. Cooley, and P. Grigsby, “Background spectral library for Fort A.P. Hill Virginia,” Proc. SPIE 5544, 35-46 (2004).
[CrossRef]

D. Manolakis and D. Marden, “Dimensionality reduction of hyperspectral imaging data using local principal component transforms,” Proc. SPIE 5425, 393-401 (2004).
[CrossRef]

M. Rossacci, D. Manolakis, J. Cipar, R. Lockwood, T. Cooley, and J. Jacobson, “Effects of dimensionality reduction on the statistical distribution of hyperspectral backgrounds,” Proc. SPIE 6302, 63020H (2006).
[CrossRef]

S. Adler-Golden, M. L. Matthew, L. Bernstein, R. Levine, A. Berk, S. Richtsmeier, P. Acharya, G. Anderson, J. W. Felde, J. Gardner, M. Hoke, L. Jeong, B. Pukall, A. Ratkowski, H. hua, and K. Burke, “Atmospheric correction for short-wave spectral imagery,”Proc. SPIE 3753, 61-69 (1999).
[CrossRef]

M. Matthew, S. Adler-Golden, A. Berk, G. Felde, G. Anderson, D. Gorodetzky, S. Paswaters, and M. Shippert, “Atmospheric correction of spectral imagery: Evaluation of the FLAASH algorithm with AVIRIS data,” Proc. SPIE 5093, 474-482 (2003).
[CrossRef]

M. Bernhardt, J. Heather, and O. Watkins, “Hyperspectral clutter statistics, generative models, and anomaly detection,” Proc. SPIE 6233, 623321 (2006).
[CrossRef]

D. Marden and D. Manolakis, “Modeling hyperspectral imaging sata using elliptically contoured distributions,” Proc. SPIE 5093, 253-262 (2003).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, “On the statistics of hyperspectral imaging data,” Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

Remote Sens. Environ. (1)

R. O. Green, M. L. Eastwood, C. M. Sarture, T. G. Chrien, M. Aronsson, B. J. Chippendale, J. A. Faust, B. E. Pavri, C. J. Chovit, M. Solis, M. R. Olah, and O. Williams, “Imaging spectroscopy and the airborne visible/infrared imaging spectrometer (AVIRIS),” Remote Sens. Environ. 65, 227-248 (1998).
[CrossRef]

Other (8)

S. Golden-Adler, A. Berk, L. S. Bernstein, S. Richtsmeier, P. K. Acharya, M. W. Matthew, G. P. Anderson, C. L. Allred, L. S. Jeong, and J. H. Chetwynd, “FLAASH, A MODTRAN4 atmospheric correction package for hyperspectral data retrievals and simulations,” (Jet Propulsion Laboratory, 1998), pp. 97-21.

D. Marden and D. Manolakis, “Statistical modeling of hyperspectral imaging data and their applications,” Tech. Rep. HTAp-16 (Lincoln Laboratory, 2004).

Strictly speaking Δ is the Mahalanobis distance and Δ2 is the squared Mahalanobis distance; however, for simplicity, the term Mahalanobis distance is used in both cases. The exact meaning should be clear from the context.

S. Kotz and S. Nadarajah, Multivariate t-Distributions and Their Applications (Cambridge University Press, 2004).

T. W. Anderson, An Introduction to Multivariate Statistical Analysis, 3rd ed. (Wiley, 2003),

K. T. Fang, S. Kotz, and K. W. Ng, Symmetric Multivariate and Related Distributions (Chapman and Hall, 1990).

J. B. Adams, M. O. Smith, and A. R. Gillespie, “Imaging spectroscopy: Interpretation based on spectral mixture analysis,” in Remote Geochemical Analysis: Elemental and Mineralogical Composition C. M. Pieters and P. A. J. Englert, eds. (Cambridge University Press, 1993), pp. 145-166.

R. Gnanadesikan, Methods for Statistical Data Analysis of Multivariate Observations, 2nd ed. (Wiley, 1997),

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Figures (12)

Fig. 1
Fig. 1

Estimated probability density functions and pairs of scatter plots for the random variables representing a spherically invariant random vector x t 5 ( 0 , I , 100 ) in polar coordinates. Clearly, the polar coordinates are pairwise uncorrelated, and each empirical distribution resembles the underlying theoretical distribution.

Fig. 2
Fig. 2

Modeling the distribution of Mahalanobis distance using the F-mixture (12). The corresponding spectral data can be modeled using Eq. (11).

Fig. 3
Fig. 3

A. P. Hill AVIRIS data and the land cover classes used for the evaluation of statistical background characterization models.

Fig. 4
Fig. 4

Visual evaluation of the elliptical symmetry characteristics of AVIRIS HSI data from the coniferous forest class. We clearly see that the first five principal components, which capture almost all background variability, can be modeled by a multivariate distribution with elliptical contours.

Fig. 5
Fig. 5

Empirical probability of exceedance for the All Loblolly Pine plantation class (stair-step) with theoretical exceedance curves for the normal and t-elliptically contoured distribution with differing degrees of freedom.

Fig. 6
Fig. 6

Mixture model components for the All Loblolly Pine Plantations class.

Fig. 7
Fig. 7

Mahalanobis distance distributions (red curves online) in reduced principal component space for the Green Agricultural Field for p = 10 155 in steps of 3. The left and right thick curves are dimensionality ( p = 155 ) and dimensionality ( p = 10 ), respectively.

Fig. 8
Fig. 8

Theoretical chi-square distributions for the Green Agricultural Field data set under Gaussianity assumption. The left and right thck curves are dimensionality ( p = 155 ) and dimensionality ( p = 10 ), respectively.

Fig. 9
Fig. 9

Mahalanobis distance distributions resulting from aggregating spectral bands of the Green Agricultural Field data set. The black curve is the full dimensionality case ( p = 155 ).

Fig. 10
Fig. 10

Direct comparison of Mahalanobis distance distributions derived from band aggregation and PCA techniques applied to the Green Agricultural Field data set for dimensionality p = 49 . The black curve is the full dimensionality case ( p = 155 ).

Fig. 11
Fig. 11

Variation in tail degree of freedom for data sets 1–9 from modeling the MTI sensor by aggregating AVIRIS sensor bands.

Fig. 12
Fig. 12

PCA-derived (triangle-line curves) and band aggregation-derived (solid squares) tail degree of freedom as a function of dimensionality for selected hyperspectral tree backgrounds. The MTI data model dimensionality ( p = 9 ) and full dimensionality AVIRIS ( p = 155 ) cases are also shown.

Tables (3)

Tables Icon

Table 1 Comparison of Tail Heaviness for Land Cover Classes Investigated in This Study

Tables Icon

Table 2 Comparison of Tail Heaviness for Spatial Block Regions

Tables Icon

Table 3 MTI Band Characteristics

Equations (30)

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x = [ x 1 x 2 x p ] T ,
f ( x ) = m = 1 M π m f m ( x ) ,
f ( x ) = 1 ( 2 π ) p / 2 | Σ | 1 / 2 exp [ 1 2 ( x μ ) T Σ 1 ( x μ ) ] ,
μ = E ( x ) ,
Σ = E [ ( x μ ) ( x μ ) T ] .
x N p ( μ , Σ ) .
Δ 2 ( x ) = ( x μ ) T Σ 1 ( x μ )
x N p ( μ , Σ ) Δ 2 ( x ) χ p 2 .
x = y ( s ν ) 1 / 2 + μ = y s / ν + μ .
f ( x ) = Γ ( p + v 2 ) ( π v ) p 2 Γ ( v 2 ) | R | [ 1 + 1 v ( x μ ) T R 1 ( x μ ) ] p + v 2 ,
E ( x ) = μ , ν > 1 ,
Cov ( x ) = Σ = ν ν 2 R , ν > 2.
1 p δ 2 ( x ) = 1 p ( x μ ) T R 1 ( x μ ) F p , ν .
1 p ν ν 2 ( x μ ) T Σ 1 ( x μ ) F p , ν .
f ( x ) = c p | C | 1 / 2 g [ ( x μ ) T C 1 ( x μ ) ] ,
x ECD p ( μ , C ) z = U T ( x μ ) ECD p ( 0 , I ) .
r = z 1 2 + z 2 2 + + z p 2 , cos θ 1 = z 1 / r , 0 < θ 1 < π , cos θ k = z k z k 1 tan θ k 1 , 0 < θ k < π , ( 2 k p 2 ) tan θ p 1 = z p / z p 1 , π < θ k 1 < π .
f ( r ) = r p 1 2 ( p / 2 ) 1 Γ ( p / 2 ) g ( r 2 ) ,
f k ( θ k ) = Γ [ ( p k + 1 ) / 2 ] π Γ [ ( p k ) / 2 ] sin p 1 k ( θ k ) , 0 < θ k < π ,
f p 1 ( θ p 1 ) = ( 2 π ) 1 , π < θ p 1 < π .
r 2 = z T z = ( x μ ) T Σ 1 ( x μ )
μ ^ = 1 n i = 1 n x i ,
Σ ^ = 1 n i = 1 n ( x i μ ^ ) ( x i μ ^ ) T ,
x w t p ( ν 1 , μ , R ) + ( 1 w ) t p ( ν 2 , μ , R ) , 0 w 1 ,
δ 2 w F p , ν 1 + ( 1 w ) F p , ν 2 .
D = i = 1 K | [ F N 1 ( P i ) F 1 ( P i ) ] | ,
Δ 2 = ( x μ ) T Σ 1 ( x μ ) .
Σ 1 = Q Λ 1 Q T = i = 1 p 1 λ i q i q i T ,
y = Q T ( x μ )
Δ p 2 = y T Λ 1 y = i = 1 p y i 2 λ i ,

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