Abstract

The matched filter is a widely used detector in hyperspectral detection applications because of its simplicity and its efficiency in practical situations. We propose to estimate its performance with respect to the number of spectral bands. These spectral bands are selected thanks to a genetic algorithm in order to optimize the contrast between the target and the background in the detection plane. Our band selection method can be used to optimize not only the position but also the linewidth of the spectral bands. The optimized contrast always increases with the number of selected bands. However, in practical situations, the target spectral signature has to be estimated from the image. We show that in the presence of estimation error, the maximum number of bands may not always be the best choice in terms of detection performance.

© 2011 Optical Society of America

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  1. J. C. Harsanyi and C. I. Chang, “Detection of subpixel signatures in hyperspectral image sequences,” in Proceedings of the American Society for Photogrammetry and Remote Sensing (1994), pp. 236–247.
  2. J. C. Harsanyi and C. I. Chang, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785 (1994).
    [CrossRef]
  3. X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
    [CrossRef]
  4. D. G. Manolakis and G. A. Shaw, “Detection algorithms for hyperspectral imaging applications,” IEEE Signal Process. Mag. 19, 29–43 (2002).
    [CrossRef]
  5. D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).
  6. D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
    [CrossRef]
  7. J. C. Price, “Band selection procedure for multispectral scanners,” Appl. Opt. 33, 3281–3288 (1994).
    [CrossRef] [PubMed]
  8. J. Karlholm and I. Renhorn, “Wavelength band selection method for multispectral target detection,” Appl. Opt. 41, 6786–6795 (2002).
    [CrossRef] [PubMed]
  9. S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
    [CrossRef]
  10. J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
    [CrossRef]
  11. D. Landgrebe, “Hyperspectral image data analysis as a high dimensional signal processing problem,” IEEE Signal Process. Mag. 19, 17–28 (2002).
    [CrossRef]
  12. F. Goudail, N. Roux, I. Baarstad, T. Løke, P. Kaspersen, M. Alouini, and X. Normandin, “Some practical issues in anomaly detection and exploitation of regions of interest in hyperspectral images,” Appl. Opt. 45, 5223–5236 (2006).
    [CrossRef] [PubMed]
  13. G. Hughes, “On the mean accuracy of statistical pattern recognizers,” IEEE Trans. Inf. Theory. 14, 55–63 (1968).
    [CrossRef]
  14. S. Kay, Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory (Prentice-Hall, 1998).
  15. J. Theiler and K. Glocer, “Sparse linear filters for detection and classification in hyperspectral imagery,” Proc. SPIE 6233, 62330H (2006).
    [CrossRef]
  16. C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
    [CrossRef]
  17. E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
    [CrossRef]
  18. C. I. Chang and S. Wang, “Constrained band selection for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 44, 1575–1585 (2006).
    [CrossRef]
  19. S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
    [CrossRef]
  20. S. B. Serpico and L. Bruzzone, “A new search algorithm for feature selection in hyperspectral remote sensing images,” IEEE Trans. Geosci. Remote Sens. 39, 1360–1367 (2001).
    [CrossRef]
  21. D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
    [CrossRef]
  22. W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection,” Pattern Recogn. Lett. 10, 335–347 (1989).
    [CrossRef]
  23. M. Kudo and J. Sklansky, “Comparison of algorithms that select features for pattern classifiers,” Pattern Recogn. 33, 25–41 (2000).
    [CrossRef]
  24. D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).
  25. M. K. Griffin and H. K. Burke, “Compensation of hyperspectral data for atmospheric effects,” Lincoln Lab. J. 14, 29–54 (2003).
  26. R. Chattamvelli and R. Shanmugam, “Computing the non-central beta distribution function,” Appl. Statist. 46, 146–156 (1997).
    [CrossRef]

2010

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

2006

F. Goudail, N. Roux, I. Baarstad, T. Løke, P. Kaspersen, M. Alouini, and X. Normandin, “Some practical issues in anomaly detection and exploitation of regions of interest in hyperspectral images,” Appl. Opt. 45, 5223–5236 (2006).
[CrossRef] [PubMed]

J. Theiler and K. Glocer, “Sparse linear filters for detection and classification in hyperspectral imagery,” Proc. SPIE 6233, 62330H (2006).
[CrossRef]

C. I. Chang and S. Wang, “Constrained band selection for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 44, 1575–1585 (2006).
[CrossRef]

2005

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

2004

D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
[CrossRef]

2003

E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
[CrossRef]

M. K. Griffin and H. K. Burke, “Compensation of hyperspectral data for atmospheric effects,” Lincoln Lab. J. 14, 29–54 (2003).

D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).

2002

D. Landgrebe, “Hyperspectral image data analysis as a high dimensional signal processing problem,” IEEE Signal Process. Mag. 19, 17–28 (2002).
[CrossRef]

D. G. Manolakis and G. A. Shaw, “Detection algorithms for hyperspectral imaging applications,” IEEE Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

J. Karlholm and I. Renhorn, “Wavelength band selection method for multispectral target detection,” Appl. Opt. 41, 6786–6795 (2002).
[CrossRef] [PubMed]

2001

S. B. Serpico and L. Bruzzone, “A new search algorithm for feature selection in hyperspectral remote sensing images,” IEEE Trans. Geosci. Remote Sens. 39, 1360–1367 (2001).
[CrossRef]

2000

M. Kudo and J. Sklansky, “Comparison of algorithms that select features for pattern classifiers,” Pattern Recogn. 33, 25–41 (2000).
[CrossRef]

1999

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

1998

S. Kay, Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory (Prentice-Hall, 1998).

1997

R. Chattamvelli and R. Shanmugam, “Computing the non-central beta distribution function,” Appl. Statist. 46, 146–156 (1997).
[CrossRef]

1994

J. C. Price, “Band selection procedure for multispectral scanners,” Appl. Opt. 33, 3281–3288 (1994).
[CrossRef] [PubMed]

J. C. Harsanyi and C. I. Chang, “Detection of subpixel signatures in hyperspectral image sequences,” in Proceedings of the American Society for Photogrammetry and Remote Sensing (1994), pp. 236–247.

J. C. Harsanyi and C. I. Chang, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785 (1994).
[CrossRef]

1993

X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
[CrossRef]

S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
[CrossRef]

1989

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection,” Pattern Recogn. Lett. 10, 335–347 (1989).
[CrossRef]

1968

G. Hughes, “On the mean accuracy of statistical pattern recognizers,” IEEE Trans. Inf. Theory. 14, 55–63 (1968).
[CrossRef]

Alouini, M.

Althouse, M. L. G.

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

Arzuaga-Cruz, E.

E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
[CrossRef]

Baarstad, I.

Barnes, J. W.

D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
[CrossRef]

Bruzzone, L.

S. B. Serpico and L. Bruzzone, “A new search algorithm for feature selection in hyperspectral remote sensing images,” IEEE Trans. Geosci. Remote Sens. 39, 1360–1367 (2001).
[CrossRef]

Burke, H. K.

M. K. Griffin and H. K. Burke, “Compensation of hyperspectral data for atmospheric effects,” Lincoln Lab. J. 14, 29–54 (2003).

Chang, C. I.

C. I. Chang and S. Wang, “Constrained band selection for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 44, 1575–1585 (2006).
[CrossRef]

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

J. C. Harsanyi and C. I. Chang, “Detection of subpixel signatures in hyperspectral image sequences,” in Proceedings of the American Society for Photogrammetry and Remote Sensing (1994), pp. 236–247.

J. C. Harsanyi and C. I. Chang, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785 (1994).
[CrossRef]

Chattamvelli, R.

R. Chattamvelli and R. Shanmugam, “Computing the non-central beta distribution function,” Appl. Statist. 46, 146–156 (1997).
[CrossRef]

Cooley, T.

D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
[CrossRef]

Crawford, M. M.

D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
[CrossRef]

De Backer, S.

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

Debruyn, W.

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

Du, Q.

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

Ferrec, Y.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

Glocer, K.

J. Theiler and K. Glocer, “Sparse linear filters for detection and classification in hyperspectral imagery,” Proc. SPIE 6233, 62330H (2006).
[CrossRef]

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

Goudail, F.

Griffin, M. K.

M. K. Griffin and H. K. Burke, “Compensation of hyperspectral data for atmospheric effects,” Lincoln Lab. J. 14, 29–54 (2003).

Harsanyi, J. C.

J. C. Harsanyi and C. I. Chang, “Detection of subpixel signatures in hyperspectral image sequences,” in Proceedings of the American Society for Photogrammetry and Remote Sensing (1994), pp. 236–247.

J. C. Harsanyi and C. I. Chang, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785 (1994).
[CrossRef]

Hughes, G.

G. Hughes, “On the mean accuracy of statistical pattern recognizers,” IEEE Trans. Inf. Theory. 14, 55–63 (1968).
[CrossRef]

Jacobson, J.

D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
[CrossRef]

Jimenez-Rodriguez, L. O.

E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
[CrossRef]

Karlholm, J.

Kaspersen, P.

Kay, S.

S. Kay, Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory (Prentice-Hall, 1998).

Kempeneers, P.

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

Korycinski, D.

D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
[CrossRef]

Kudo, M.

M. Kudo and J. Sklansky, “Comparison of algorithms that select features for pattern classifiers,” Pattern Recogn. 33, 25–41 (2000).
[CrossRef]

Landgrebe, D.

D. Landgrebe, “Hyperspectral image data analysis as a high dimensional signal processing problem,” IEEE Signal Process. Mag. 19, 17–28 (2002).
[CrossRef]

Lockwood, R.

D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
[CrossRef]

Løke, T.

Lonnoy, J.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

Manolakis, D.

D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).

Manolakis, D. G.

D. G. Manolakis and G. A. Shaw, “Detection algorithms for hyperspectral imaging applications,” IEEE Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
[CrossRef]

Marden, D.

D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).

Minet, J.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

Normandin, X.

Péalat, M.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

Peterson, J. R.

S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
[CrossRef]

Price, J. C.

Reed, I. S.

X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
[CrossRef]

Renhorn, I.

Roux, N.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

F. Goudail, N. Roux, I. Baarstad, T. Løke, P. Kaspersen, M. Alouini, and X. Normandin, “Some practical issues in anomaly detection and exploitation of regions of interest in hyperspectral images,” Appl. Opt. 45, 5223–5236 (2006).
[CrossRef] [PubMed]

Scheunders, P.

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

Serpico, S. B.

S. B. Serpico and L. Bruzzone, “A new search algorithm for feature selection in hyperspectral remote sensing images,” IEEE Trans. Geosci. Remote Sens. 39, 1360–1367 (2001).
[CrossRef]

Shanmugam, R.

R. Chattamvelli and R. Shanmugam, “Computing the non-central beta distribution function,” Appl. Statist. 46, 146–156 (1997).
[CrossRef]

Shaw, G. A.

D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).

D. G. Manolakis and G. A. Shaw, “Detection algorithms for hyperspectral imaging applications,” IEEE Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

Siedlecki, W.

W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection,” Pattern Recogn. Lett. 10, 335–347 (1989).
[CrossRef]

Sklansky, J.

M. Kudo and J. Sklansky, “Comparison of algorithms that select features for pattern classifiers,” Pattern Recogn. 33, 25–41 (2000).
[CrossRef]

W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection,” Pattern Recogn. Lett. 10, 335–347 (1989).
[CrossRef]

Stearns, S. D.

S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
[CrossRef]

Stocker, A. D.

X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
[CrossRef]

Sun, T. L.

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

Taboury, J.

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

Theiler, J.

J. Theiler and K. Glocer, “Sparse linear filters for detection and classification in hyperspectral imagery,” Proc. SPIE 6233, 62330H (2006).
[CrossRef]

Vélez-Reyes, M.

E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
[CrossRef]

Wang, S.

C. I. Chang and S. Wang, “Constrained band selection for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 44, 1575–1585 (2006).
[CrossRef]

Wilson, B. E.

S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
[CrossRef]

Yu, X.

X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
[CrossRef]

Appl. Opt.

Appl. Statist.

R. Chattamvelli and R. Shanmugam, “Computing the non-central beta distribution function,” Appl. Statist. 46, 146–156 (1997).
[CrossRef]

IEEE Geosci. Remote Sens. Lett.

S. De Backer, P. Kempeneers, W. Debruyn, and P. Scheunders, “Band selection for hyperspectral remote sensing,” IEEE Geosci. Remote Sens. Lett. 2, 319–323 (2005).
[CrossRef]

IEEE Signal Process. Mag.

D. G. Manolakis and G. A. Shaw, “Detection algorithms for hyperspectral imaging applications,” IEEE Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

D. Landgrebe, “Hyperspectral image data analysis as a high dimensional signal processing problem,” IEEE Signal Process. Mag. 19, 17–28 (2002).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

C. I. Chang, Q. Du, T. L. Sun, and M. L. G. Althouse, “A joint band prioritization and band-decorrelation approach to band selection for hyperspectral image classification,” IEEE Trans. Geosci. Remote Sens. 37, 2631–2641 (1999).
[CrossRef]

C. I. Chang and S. Wang, “Constrained band selection for hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 44, 1575–1585 (2006).
[CrossRef]

J. C. Harsanyi and C. I. Chang, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785 (1994).
[CrossRef]

S. B. Serpico and L. Bruzzone, “A new search algorithm for feature selection in hyperspectral remote sensing images,” IEEE Trans. Geosci. Remote Sens. 39, 1360–1367 (2001).
[CrossRef]

IEEE Trans. Inf. Theory.

G. Hughes, “On the mean accuracy of statistical pattern recognizers,” IEEE Trans. Inf. Theory. 14, 55–63 (1968).
[CrossRef]

IEEE Trans. Signal Process.

X. Yu, I. S. Reed, and A. D. Stocker, “Comparative performance analysis of adaptive multispectral detectors,” IEEE Trans. Signal Process. 41, 2639–2656 (1993).
[CrossRef]

Lincoln Lab. J.

D. Manolakis, D. Marden, and G. A. Shaw, “Hyperspectral image processing for automatic target detection applications,” Lincoln Lab. J. 14, 79–116 (2003).

M. K. Griffin and H. K. Burke, “Compensation of hyperspectral data for atmospheric effects,” Lincoln Lab. J. 14, 29–54 (2003).

Pattern Recogn.

M. Kudo and J. Sklansky, “Comparison of algorithms that select features for pattern classifiers,” Pattern Recogn. 33, 25–41 (2000).
[CrossRef]

Pattern Recogn. Lett.

W. Siedlecki and J. Sklansky, “A note on genetic algorithms for large-scale feature selection,” Pattern Recogn. Lett. 10, 335–347 (1989).
[CrossRef]

Proc. SPIE

J. Theiler and K. Glocer, “Sparse linear filters for detection and classification in hyperspectral imagery,” Proc. SPIE 6233, 62330H (2006).
[CrossRef]

D. Korycinski, M. M. Crawford, and J. W. Barnes, “Adaptive feature selection for hyperspectral data analysis,” Proc. SPIE 5238, 213–225 (2004).
[CrossRef]

J. Minet, J. Taboury, M. Péalat, N. Roux, J. Lonnoy, and Y. Ferrec, “Adaptive band selection snapshot multispectral imaging in the VIS/NIR domain,” Proc. SPIE 7835, 78350W(2010).
[CrossRef]

S. D. Stearns, B. E. Wilson, and J. R. Peterson, “Dimensionality reduction by optimal band selection for pixel classification of hyperspectral imagery,” Proc. SPIE 2028, 118–127 (1993).
[CrossRef]

E. Arzuaga-Cruz, L. O. Jimenez-Rodriguez, and M. Vélez-Reyes, “Unsupervised feature extraction and band subset selection techniques based on relative entropy criteria for hyperspectral data analysis,” Proc. SPIE 5093, 462–473(2003).
[CrossRef]

Other

S. Kay, Fundamentals of Statistical Signal Processing, Volume 2: Detection Theory (Prentice-Hall, 1998).

J. C. Harsanyi and C. I. Chang, “Detection of subpixel signatures in hyperspectral image sequences,” in Proceedings of the American Society for Photogrammetry and Remote Sensing (1994), pp. 236–247.

D. G. Manolakis, R. Lockwood, T. Cooley, and J. Jacobson, “Is there a best hyperspectral detection algorithm?” SPIE Newsroom (17 June 2009).
[CrossRef]

D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning (Addison-Wesley, 1989).

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Figures (15)

Fig. 1
Fig. 1

RGB representation of the multispectral image of the observed scene.

Fig. 2
Fig. 2

Definition of the region of interest of the target.

Fig. 3
Fig. 3

Detection plane obtained with the matched filter. The contrast C between the target and the background is 33.35.

Fig. 4
Fig. 4

Filtering process.

Fig. 5
Fig. 5

Evolutionary cycle.

Fig. 6
Fig. 6

Chromosome and its corresponding filtering matrix R in the case of (a) ideal single-band filters and (b) bandpass filters.

Fig. 7
Fig. 7

Reproduction process.

Fig. 8
Fig. 8

Profiles of the four best single-band filters. Each peak is a symbolic representation of the instrumental function of the Specim ImSpector QE V10E hyperspectral imager.

Fig. 9
Fig. 9

Profiles of the four best bandpass filters.

Fig. 10
Fig. 10

Contrast between the target and the background in the detection plane versus the number of selected bands. The black dotted curve corresponds to the optimized contrast obtained with single-band filters; the red solid curve corresponds to the optimized contrast obtained with bandpass filters.

Fig. 11
Fig. 11

Maximum contrast obtained versus the number P of calculations of the contrast for two different algorithms: genetic algorithm (red solid curve) and Monte Carlo algorithm (black dotted curve). The optimization is done for K = 10 bands.

Fig. 12
Fig. 12

Contrast versus the number of selected single bands for two optimization algorithms: SFS algorithm (black dotted curve) and genetic algorithm (red solid curve). The genetic algorithm runs 100 generations of 100 elements ( P = 10 , 000 calculations of the contrast).

Fig. 13
Fig. 13

Optimization of the global normalized contrast C ¯ glob ( R max glob ) (black dotted curve) and mean of the three optimized normalized contrast C ¯ i ( R max i ) i { 1 , 2 , 3 } (red solid curve) versus the number of selected bands.

Fig. 14
Fig. 14

Mean contrast loss E { C } / C versus the number of bands K for different values of the parameter C / α 2 . Solid curves, contrast loss estimation from 1000 random draws. Dotted curves, ( C / α 2 + 1 ) / ( C / α 2 + K ) .

Fig. 15
Fig. 15

Expected contrast versus number of bands for different values of α 2 [Eq. (35)].

Tables (1)

Tables Icon

Table 1 CPU Running Time of the Band Selection Algorithms for a Selection of 10 Single Bands a

Equations (35)

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x { N ( m 0 , Γ ) under   γ 0 ( target absent ) N ( m 1 , Γ ) under   γ 1 ( target present ) ,
y = D mf ( x ) = ( m 1 - m 0 ) T Γ - 1 ( x - m 0 ) ,
y = D mf ( x ) { N ( 0 , Δ 2 ) under   γ 0 N ( Δ 2 , Δ 2 ) under   γ 1 ,
{ P FA = η + p ( y | γ 0 ) d y , P D = η + p ( y | γ 1 ) d y ,
{ m 1 = E { x | γ 1 } , m 0 = E { x | γ 0 } , Γ = E { ( x m 0 ) ( x m 0 ) T | γ 0 } .
y w = D w ( x ) = w T ( x m 0 ) ,
{ E { y w | γ 1 } = w T ( m 1 m 0 ) , E { y w | γ 0 } = 0 , var { y w | γ 0 } = E { w T ( x m 0 ) ( x m 0 ) T w | γ 0 } , = w T Γ w .
C w = [ E { y w | γ 1 } E { y w | γ 0 } ] 2 var { y w | γ 0 } = [ w T ( m 1 m 0 ) ] 2 w T Γ w .
w mf = arg max w w T Δ m   subject to   w T Γ w = 1.
y = D w mf ( x ) = ( m 1 m 0 ) T Γ 1 ( x m 0 ) .
C = C w mf = [ ( m 1 m 0 ) T Γ 1 ( m 1 m 0 ) ] 2 ( m 1 m 0 ) T Γ 1 Γ Γ 1 ( m 1 - m 0 ) = ( m 1 - m 0 ) T Γ - 1 ( m 1 - m 0 ) = Δ 2 .
{ m 1 = x 1 , m 0 = x 0 , Γ = ( x m 0 ) ( x m 0 ) T 0 ,
C ( R ) = ( m 1 m 0 ) T R ( R T Γ R ) 1 R T ( m 1 m 0 ) .
R max = arg max R R K C ( R ) .
C ¯ i ( R ) = ( m i , 1 m i , 0 ) T R ( R T Γ i R ) 1 R T ( m i , 1 m i , 0 ) ( m i , 1 m i , 0 ) T Γ i 1 ( m i , 1 m i , 0 ) .
R max i = arg max R R K C ¯ i ( R ) .
C ¯ glob ( R ) = 1 3 i = 1 3 C ¯ i ( R ) .
R max glob = arg max R R K C ¯ glob ( R ) .
y = D amf ( x ) = ( m ^ 1 m 0 ) T Γ 1 ( x m 0 ) .
{ E { y | γ 1 } = μ ^ T μ , E { y | γ 0 } = 0 , var { y | γ 0 } = μ ^ T μ ^ .
C = ( μ ^ T μ ) 2 μ ^ T μ ^ ,
= μ T μ ( μ ^ T μ ) 2 ( μ ^ T μ ^ ) ( μ T μ ) ,
= C ( μ ^ T μ ) 2 ( μ ^ T μ ^ ) ( μ T μ ) ,
μ ^ T μ = μ ^ 1 μ 1 ,
μ ^ T μ ^ = i = 1 K μ ^ i 2 .
C = C μ ^ 1 2 i = 1 K μ ^ i 2 .
E { μ ^ 1 2 i = 1 K μ ^ i 2 } = 1 K j = 1 K E { μ ^ j 2 i = 1 K μ ^ i 2 } = 1 K E { j = 1 K μ ^ j 2 i = 1 K μ ^ i 2 } = 1 K .
E { C } = C K .
m ^ 1 = 1 N i = 1 N x i .
E { m ^ 1 m 1 } = 0 ,
Cov { m ^ 1 m 1 } = 1 N Γ .
μ ^ T μ = ( ( μ 1 + α ϵ 1 ) u 1 + i = 2 K α ϵ i u i ) T μ 1 u 1 = μ 1 2 + α ϵ 1 μ 1 ,
μ ^ T μ ^ = ( μ 1 + α ϵ 1 ) u 1 + i = 2 K α ϵ i u i 2 = ( μ 1 + α ϵ 1 ) 2 + i = 2 K α 2 ϵ i 2 .
C = μ i 2 ( μ 1 + α ϵ 1 ) 2 ( μ 1 + α ϵ 1 ) 2 + i = 2 K α 2 ϵ i 2 = C × ( μ 1 / α + ϵ 1 ) 2 ( μ 1 / α + ϵ 1 ) 2 + i = 2 K ϵ i 2 = C × χ 1 , C / α 2 2 χ 1 , C / α 2 2 + χ K 1 2 ,
E { C } C × E { ( μ 1 / α + ϵ 1 ) 2 } E { ( μ 1 / α + ϵ 1 ) 2 + i = 2 K ϵ i 2 } C × C / α 2 + 1 C / α 2 + K .

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