Abstract

We present an approach to the problems of weak plume detection and sub-pixel target detection in hyperspectral imagery that operates in a two-dimensional space. In this space, one axis is a matched-filter projection of the data and the other axis is the magnitude of the residual after matched-filter subtraction. Although it is only two-dimensional, this space is rich enough to include several well-known signal detection algorithms, including the adaptive matched filter, the adaptive coherence estimator, and the finite-target matched filter. Because this space is only two-dimensional, adaptive machine learning methods can produce new plume detectors without being stymied by the curse of dimensionality. We investigate, in particular, the utility of the support vector machine for learning boundaries in this matched-filter-residual space, and compare the performance of the resulting nonlinearly adaptive detector to well-known alternatives.

© 2009 Optical Society of America

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2007 (2)

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

J. Theiler, B. Foy, and A. Fraser, "Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter," Proc. SPIE 6565, 656503-1 (2007).

2006 (2)

J. Theiler, B. R. Foy, and A. M. Fraser, "Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery," Proc. SPIE 6233, 62331U-1 (2006).

J. Theiler and B. R. Foy, "Effect of signal contamination in matched-filter detection of the signal on a cluttered background," IEEE Geosci. Remote Sens. Lett. 3, 98-102 (2006).
[CrossRef]

2005 (2)

J. Theiler, B. R. Foy, and A. M. Fraser, "Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery," Proc. SPIE 5806, 182-193 (2005).
[CrossRef]

D. Manolakis, "Taxonomy of detection algorithms for hyperspectral imaging applications," Opt. Eng. 44, 066403 (2005).
[CrossRef]

2004 (1)

D. B. Marden and D. Manolakis, "Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data," Proc. SPIE 5425, 558-572 (2004).
[CrossRef]

2003 (1)

N. B. Gallagher, B. M. Wise, and D. M. Sheen, "Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images," Analytica Chimica Acta 490, 139-152 (2003).
[CrossRef]

2002 (3)

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

S. J. Young, B. R. Johnson, and J. A. Hackwell, "An in-scene method for atmospheric compensation of thermal hyperspectral data," J. Geophys. Res. Atm. 107, 4774 (2002).
[CrossRef]

2001 (2)

S. Kraut, L. L. Scharf, and L. T. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, "On the Statistics of Hyperspectral Imaging Data," Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

1999 (2)

M. E. Winter, "N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data," Proc. SPIE 3753, 266-275 (1999).
[CrossRef]

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

1996 (1)

A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2803-2809 (1996).
[CrossRef]

1993 (2)

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

C. Lee and D. A. Landgrebe, "Analyzing high-dimensional multispectral data," IEEE Trans. Geosci. Remote Sens. 31, 792-800 (1993).
[CrossRef]

1992 (1)

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

1977 (2)

1974 (1)

I. S. Reed, J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst. 10, 853-863 (1974).
[CrossRef]

Adams, P.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Boyce, B.

A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2803-2809 (1996).
[CrossRef]

Brennan, L. E.

I. S. Reed, J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst. 10, 853-863 (1974).
[CrossRef]

Chrien, T. G.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Enmark, H. T.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Foy, B.

J. Theiler, B. Foy, and A. Fraser, "Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter," Proc. SPIE 6565, 656503-1 (2007).

Foy, B. R.

J. Theiler, B. R. Foy, and A. M. Fraser, "Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery," Proc. SPIE 6233, 62331U-1 (2006).

J. Theiler and B. R. Foy, "Effect of signal contamination in matched-filter detection of the signal on a cluttered background," IEEE Geosci. Remote Sens. Lett. 3, 98-102 (2006).
[CrossRef]

J. Theiler, B. R. Foy, and A. M. Fraser, "Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery," Proc. SPIE 5806, 182-193 (2005).
[CrossRef]

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

Fraser, A.

J. Theiler, B. Foy, and A. Fraser, "Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter," Proc. SPIE 6565, 656503-1 (2007).

Fraser, A. M.

J. Theiler, B. R. Foy, and A. M. Fraser, "Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery," Proc. SPIE 6233, 62331U-1 (2006).

J. Theiler, B. R. Foy, and A. M. Fraser, "Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery," Proc. SPIE 5806, 182-193 (2005).
[CrossRef]

Fry, H. A.

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

Fuhrmann, D. R.

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

Gallagher, N. B.

N. B. Gallagher, B. M. Wise, and D. M. Sheen, "Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images," Analytica Chimica Acta 490, 139-152 (2003).
[CrossRef]

Green, R. O.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Hackwell, J.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Hackwell, J. A.

S. J. Young, B. R. Johnson, and J. A. Hackwell, "An in-scene method for atmospheric compensation of thermal hyperspectral data," J. Geophys. Res. Atm. 107, 4774 (2002).
[CrossRef]

Hansen, E. G.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Hayden, A.

A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2803-2809 (1996).
[CrossRef]

Herr, K.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Jairam, L.

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

Johnson, B. R.

S. J. Young, B. R. Johnson, and J. A. Hackwell, "An in-scene method for atmospheric compensation of thermal hyperspectral data," J. Geophys. Res. Atm. 107, 4774 (2002).
[CrossRef]

Keim, E.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Kelly, E. J.

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

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]

Kirkland, L.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Kraut, S.

S. Kraut, L. L. Scharf, and L. T. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Landgrebe, D. A.

C. Lee and D. A. Landgrebe, "Analyzing high-dimensional multispectral data," IEEE Trans. Geosci. Remote Sens. 31, 792-800 (1993).
[CrossRef]

Lee, C.

C. Lee and D. A. Landgrebe, "Analyzing high-dimensional multispectral data," IEEE Trans. Geosci. Remote Sens. 31, 792-800 (1993).
[CrossRef]

Mallett, J. D.

I. S. Reed, J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst. 10, 853-863 (1974).
[CrossRef]

Manolakis, D.

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

D. Manolakis, "Taxonomy of detection algorithms for hyperspectral imaging applications," Opt. Eng. 44, 066403 (2005).
[CrossRef]

D. B. Marden and D. Manolakis, "Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data," Proc. SPIE 5425, 558-572 (2004).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, "On the Statistics of Hyperspectral Imaging Data," Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

Marden, D.

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, "On the Statistics of Hyperspectral Imaging Data," Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

Marden, D. B.

D. B. Marden and D. Manolakis, "Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data," Proc. SPIE 5425, 558-572 (2004).
[CrossRef]

McWhorter, L. T.

S. Kraut, L. L. Scharf, and L. T. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

Morgan, D.

Niple, E.

A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2803-2809 (1996).
[CrossRef]

Nitzberg, R.

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

Petrin, R. R.

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

Porter, W. M.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Quick, C. R.

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

Reed, I. S.

I. S. Reed, J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst. 10, 853-863 (1974).
[CrossRef]

Robey, F. C.

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

Rossacci, M.

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

Salisbury, J.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Scharf, L. L.

S. Kraut, L. L. Scharf, and L. T. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[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]

Sheen, D. M.

N. B. Gallagher, B. M. Wise, and D. M. Sheen, "Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images," Analytica Chimica Acta 490, 139-152 (2003).
[CrossRef]

Shimada, T.

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

Smith, B. W.

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

Stocker, A. D.

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

Theiler, J.

J. Theiler, B. Foy, and A. Fraser, "Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter," Proc. SPIE 6565, 656503-1 (2007).

J. Theiler, B. R. Foy, and A. M. Fraser, "Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery," Proc. SPIE 6233, 62331U-1 (2006).

J. Theiler and B. R. Foy, "Effect of signal contamination in matched-filter detection of the signal on a cluttered background," IEEE Geosci. Remote Sens. Lett. 3, 98-102 (2006).
[CrossRef]

J. Theiler, B. R. Foy, and A. M. Fraser, "Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery," Proc. SPIE 5806, 182-193 (2005).
[CrossRef]

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

Tiee, J. J.

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

Treiman, A.

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Vane, G.

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

Villeneuve, P. V.

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

Winter, M. E.

M. E. Winter, "N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data," Proc. SPIE 3753, 266-275 (1999).
[CrossRef]

Wise, B. M.

N. B. Gallagher, B. M. Wise, and D. M. Sheen, "Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images," Analytica Chimica Acta 490, 139-152 (2003).
[CrossRef]

Young, S. J.

S. J. Young, B. R. Johnson, and J. A. Hackwell, "An in-scene method for atmospheric compensation of thermal hyperspectral data," J. Geophys. Res. Atm. 107, 4774 (2002).
[CrossRef]

Zhang, D.

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

Analytica Chimica Acta (1)

N. B. Gallagher, B. M. Wise, and D. M. Sheen, "Estimation of trace vapor concentration-pathlength in plumes for remote sensing applications from hyperspectral images," Analytica Chimica Acta 490, 139-152 (2003).
[CrossRef]

Appl. Opt. (1)

A. Hayden, E. Niple, and B. Boyce, "Determination of trace-gas amounts in plumes by the use of orthogonal digital filtering of thermal-emission spectra," Appl. Opt. 35, 2803-2809 (1996).
[CrossRef]

Appl. Spectrosc. (2)

IEEE Geosci. Remote Sens. Lett. (1)

J. Theiler and B. R. Foy, "Effect of signal contamination in matched-filter detection of the signal on a cluttered background," IEEE Geosci. Remote Sens. Lett. 3, 98-102 (2006).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (2)

I. S. Reed, J. D. Mallett, and L. E. Brennan, "Rapid convergence rate in adaptive arrays," IEEE Trans. Aerosp. Electron. Syst. 10, 853-863 (1974).
[CrossRef]

F. C. Robey, D. R. Fuhrmann, E. J. Kelly, and R. Nitzberg, "A CFAR adaptive matched filter detector," IEEE Trans. Aerosp. Electron. Syst. 28, 208-216 (1992).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

C. Lee and D. A. Landgrebe, "Analyzing high-dimensional multispectral data," IEEE Trans. Geosci. Remote Sens. 31, 792-800 (1993).
[CrossRef]

IEEE Trans. Signal Process. (1)

S. Kraut, L. L. Scharf, and L. T. McWhorter, "Adaptive subspace detectors," IEEE Trans. Signal Process. 49, 1-16 (2001).
[CrossRef]

J. Geophys. Res. Atm. (1)

S. J. Young, B. R. Johnson, and J. A. Hackwell, "An in-scene method for atmospheric compensation of thermal hyperspectral data," J. Geophys. Res. Atm. 107, 4774 (2002).
[CrossRef]

Opt. Eng. (1)

D. Manolakis, "Taxonomy of detection algorithms for hyperspectral imaging applications," Opt. Eng. 44, 066403 (2005).
[CrossRef]

Proc. SPIE (9)

J. Theiler, B. R. Foy, and A. M. Fraser, "Nonlinear signal contamination effects for gaseous plume detection in hyperspectral imagery," Proc. SPIE 6233, 62331U-1 (2006).

J. Theiler, B. R. Foy, and A. M. Fraser, "Characterizing non-Gaussian clutter and detecting weak gaseous plumes in hyperspectral imagery," Proc. SPIE 5806, 182-193 (2005).
[CrossRef]

D. Manolakis, D. Marden, J. Kerekes, and G. Shaw, "On the Statistics of Hyperspectral Imaging Data," Proc. SPIE 4381, 308-316 (2001).
[CrossRef]

B. R. Foy, R. R. Petrin, C. R. Quick, T. Shimada, and J. J. Tiee, "Comparisons between hyperspectral passive and multispectral active sensor measurements." Proc. SPIE 4722, 98-109 (2002).
[CrossRef]

D. Manolakis, L. Jairam, D. Zhang, and M. Rossacci, "Statistical models for LWIR hyperspectral backgrounds and their applications in chemical agent detection," Proc. SPIE 6565, 656525-1, (2007).
[CrossRef]

P. V. Villeneuve, H. A. Fry, J. Theiler, B. W. Smith, and A. D. Stocker, "Improved matched-filter detection techniques," Proc. SPIE 3753, 278-285 (1999).
[CrossRef]

M. E. Winter, "N-FINDR: an algorithm for fast autonomous spectral end-member determination in hyperspectral data," Proc. SPIE 3753, 266-275 (1999).
[CrossRef]

J. Theiler, B. Foy, and A. Fraser, "Beyond the adaptive matched filter: nonlinear detectors for weak signals in high-dimensional clutter," Proc. SPIE 6565, 656503-1 (2007).

D. B. Marden and D. Manolakis, "Using elliptically contoured distributions to model hyperspectral imaging data and generate statistically similar synthetic data," Proc. SPIE 5425, 558-572 (2004).
[CrossRef]

Remote Sens. Environ. (2)

G. Vane, R. O. Green, T. G. Chrien, H. T. Enmark, E. G. Hansen, and W. M. Porter, "The Airborne Visible/ Infrared Imaging Spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
[CrossRef]

L. Kirkland, K. Herr, E. Keim, P. Adams, J. Salisbury, J. Hackwell, and A. Treiman, "First use of an airborne thermal infrared hyperspectral scanner for compositional mapping," Remote Sens. Environ. 80, 447-59 (2002).
[CrossRef]

Other (16)

S. J. Young, "Detection and Quantification of Gases in Industrial-Stack Plumes Using Thermal-Infrared Hyperspectral Imaging," Tech. Rep. ATR-2002(8407)-1, The Aerospace Corporation (2002).

A. Schaum and A. Stocker, "Spectrally-selective target detection," in Proc. Intl. Symp. Spectral Sens. Research, San Diego, B. A. Mandel, ed., p. 23. Available at http://leupold.gis.usu.edu/docs/protected/procs/isssr/1997/.

J. A. Richards and X. Jia, Remote Sensing Digital Image Analysis (Springer, New York, 2006).
[CrossRef]

J. B. Adams and A. R. Gillespie, Remote Sensing of Landscapes with Spectral Images (Cambridge Univ. Press, New York, 2006).
[CrossRef]

L. L. Scharf, Statistical Signal Processing (Addison-Wesley, Reading, MA, 1990).

J. Schott, Remote Sensing: the Image Chain Approach (Oxford University Press, New York, 1997).

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

AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) Free Standard Data Products, Jet Propulsion Laboratory (JPL), National Aeronautics and Space Administration (NASA), http://aviris.jpl.nasa.gov/html/aviris.freedata.html.

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, New York, 1974).

A. Schaum, "Hyperspectral Target Detection using a Bayesian Likelihood Ratio Test," Proc. IEEE Aerospace Conf. 3, 1537-1540 (2002).

A. C. Rencher, Linear Models in Statistics (Wiley, New York, 2000).

N. R. Draper and H. Smith, Applied Regression Analysis (Wiley, New York, 1998).

B. Scholkopf and A. J. Smola, Learning with Kernels (MIT Press, Cambridge, MA, 2002).

C.-C. Chang and C.-J. Lin, LIBSVM: a library for support vector machines (2001). Software available at www.csie.ntu.edu.tw/?cjlin/libsvm.

T. J. Cudahy, J. Wilson, R. Hewson, P. Linton, P. Harris, M. Sears, K. Okada, and J. A. Hackwell, "Mapping variations in plagioclase felspar mineralogy using airborne hyperspectral TIR imaging data," in Proc. IEEE 2001 Intl. Geosci. Remote Sensing Symp., Sydney, Australia, T. Milne and B. Cechet, eds., pp. 730-732 (IEEE, Piscataway, NJ, 2001).

J. Theiler and B. Foy, "EC-GLRT: Detecting weak plumes in non-Gaussian hyperspectral clutter using an elliptically-contoured generalized likelihood ratio test," Proc. IEEE Intl. Geosci. Remote Sensing Symp. (2008).

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Figures (10)

Fig. 1.
Fig. 1.

MFR plots and associated ROC curves for detection using simulated data with matched pairs chosen so that SCR=10. (a) Gaussian (b) EC data with ν=3. (a,b) Lines drawn to show AMF and t contours with thresholds for P fa=0.005. For the heavy tailed distribution, the R values spread out to the right. Note also how the t statistic boundary more closely matches the upper edge of the data cloud for EC data. (c) ROC curves for Gaussian data and for (d) EC data. Here, the vertical dashed line corresponds to P fa=0.005. The t statistic is better than AMF for fat-tailed data at low P fa because its contours closely hug the upper edge of the distribution of plume-free pixels. At higher P fa, there is a crossover and AMF performs better.

Fig. 2.
Fig. 2.

Graphical illustration of nonlinear MFR detection algorithm. (a) Data plotted in MFR space. (b) The matched pair in the same MFR space, with a curved decision boundary determined by SVM. P fa=3.6×10-3. (c) A few points from the original data set (or a new data set) are re-classified according to the decision boundary (circled points). In this example, N=128 and m=2×104.

Fig. 3.
Fig. 3.

Decision boundaries for matched pair EC data drawn by SVM. (a) Linear kernel. (b) 2nd order polynomial kernel. (c) rbf kernel. Curves drawn for a similar set of Pfa values, P fa=0.02 to 0.4.

Fig. 4.
Fig. 4.

Data used to construct a simulated LWIR dataset. (a) Spectra of the background signatures. “Ampl. modulation” is incorporated by multiplication to capture the variability of the of the background spectra (see text). (b) Spectrum of the target signature. The chemical is chlorodifluoromethane.

Fig. 5.
Fig. 5.

Spectra in the LWIR simulation. (a) Mean radiance spectrum in units of µWcm -2 sr -1(cm -1)-1. The dashed curves show mean ±1 standard deviation resulting from emissivity variability. (b) Typical brightness temperature spectra of off-plume and on-plume pixels; the difference is barely visible. (c) Difference between spectra in panel (b), showing magnitude of simulated random instrument noise. The smooth curve is the target spectrum added to plume pixels in the matched pair, magnified 10 times and offset by 0.2 K.

Fig. 6.
Fig. 6.

(a) MFR plot for synthetic LWIR data (randomly selected points shown for clarity). The decision boundaries determined by SVM analysis drawn for P fa=0.005,0.076,0.14,0.21,0.30,0.65 (top to bottom). rbf kernel used in SVM. (b) Decision boundaries for the t statistic and (c) AMF detector at the same set of P fa values.

Fig. 7.
Fig. 7.

ROC curves for detection of plume signature in synthetic LWIR data. Curves plotted for nonlinear MFR (SVM), t statistic, and AMF. (a) Full range of detection rates. (b) Expanded view showing region where the nonlinear detection algorithm is the best performer. (c) Low P fa region on a log scale.

Fig. 8.
Fig. 8.

A sample AVIRIS dataset. (a) Broadband image, containing 10201 pixels. (b) Spectrum of the target signature (dashed) and of five representative pixels. (c) Normal probability plot of the MF values. The straight line refers to a Gaussian distribution.

Fig. 9.
Fig. 9.

(a) MFR plot for the AVIRIS data of Fig. 8(a). Decision boundaries plotted for the t statistic, the AMF, FTMF, and the curved boundary produced by SVM-MFR detector. The target fraction f=0.2 is large for purposes of clarity. P fa=0.02 for all detectors. (b) Detection performance for the four algorithms in the low P fa regime. Target fraction f=0.08.

Fig. 10.
Fig. 10.

Power plot of detection performance for AVIRIS data. Detection rate as a function of SCR for the matched pair. For all 4 detectors, the false alarm rate is fixed at P fa=9.6×10-3. The SVM detector was trained on a matched-pair set corresponding to P d=0.2, but it performs well for a range of SCR values.

Tables (1)

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Table 1. Nonlinear MFR Detection Algorithm

Equations (41)

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x=εs+w
x=εs+w
x=fr+(1f)w
x=fs+(1f)w
MF=qTx=sTC1xsTC1s
R=xTC1x(qTx)2
t=MFRN1
MF2+R2=xTC1x
xon=xoff+εmps,
xon=(1fmp)xoff+fmps.
εmp=nsTC1s
DFTMF(x,f)=Nln(1f)2f(1f)2[(2f)xTC1x2sTC1x+fsTC1s]
2(1f̂)=βγ+[(βγ)2+4(α2β+γ)]12
x=Hθ+w
E{w}=0
E{wwT}=C (known)
RSS=C12(xHθ)2
=(xHθ)TC1(xHθ)
θ̂=(HTC1H)1 HT C1 x
SSE=(xHθ̂)TC1(xHθ̂)
=(xx̂)TC1 (xx̂)
=xTC1x+x̂TC1x̂2x̂TC1x
x̂TC1x̂=x̂TC1x
SSE=xTC1xx̂TC1x=SSTSSR
F(x)SSRSSENpp
F(x)=x̂TC1xxTC1xx̂TC1xNpp
=xTC1H(HTC1H)1HTC1xxTC1xxTC1H(HTC1H)1HTC1xNpp
F(x)=(sTC1x)2sTC1sxTC1x(sTC1x)2sTC1s(N1)
q=1sTC1sC1s
F(x)=(qTx)2xTC1x(qTx)2(N1)
t(x)=qTxxTC1x(qTx)2 N1
MF=qTx=sTC1xsTC1s
R=xTC1x(qTx)2
ACE=sTC1xsTC1sxTC1x
=tNtN2+1=(1tN2+1)12
MF=1mi=1mqTxi=qT(1mi=1mwi+εmps)=εmpqTs
=εmp(C1ssTC1s)Ts=εmpsTC1s
=SCR
var(qTw)=1mi=1m(qTw)2=1mi=1mqTwwTq=qT(1mi=1mwwT)q=qTCq
SCR=(εqTs)2var(qTw)=ε2sTC1s
E{SCR(C)SCR(Ctrue)}=1Nm

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