Abstract

This paper describes a new wavelet-based anomaly detection technique for a dual-band forward-looking infrared (FLIR) sensor consisting of a coregistered longwave (LW) with a midwave (MW) sensor. The proposed approach, called the wavelet-RX (Reed–Xiaoli) algorithm, consists of a combination of a two-dimensional (2D) wavelet transform and a well-known multivariate anomaly detector called the RX algorithm. In our wavelet-RX algorithm, a 2D wavelet transform is first applied to decompose the input image into uniform subbands. A subband-image cube is formed by concatenating together a number of significant subbands (high-energy subbands). The RX algorithm is then applied to the subband-image cube obtained from a wavelet decomposition of the LW or MW sensor data. In the case of the dual band, the RX algorithm is applied to a subband-image cube constructed by concatenating together the high-energy subbands of the LW and MW subband-image cubes. Experimental results are presented for the proposed wavelet-RX and the classical constant false alarm rate (CFAR) algorithm for detecting anomalies (targets) in a single broadband FLIR (LW or MW) or in a coregistered dual-band FLIR sensor. The results show that the proposed wavelet-RX algorithm outperforms the classical CFAR detector for both single-band and dual-band FLIR sensors.

© 2010 Optical Society of America

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  1. H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
    [CrossRef]
  2. D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
    [CrossRef]
  3. S. Kuttikkad and R. Chellappa, “Non-Gaussian CFAR techniques for target detection in high resolution SAR images,” in Proceedings of the International Conference on Image Processing (IEEE, 1994), pp. 910–914.
  4. B. Bhanu, “Automatic target recognition: state of the art survey,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 364–379 (1986).
    [CrossRef]
  5. A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
    [CrossRef]
  6. S. Z. Der and R. Chellappa, “Probe-based automatic target recognition in infrared imagery,” IEEE Trans. Image Process. 6, 92–102 (1997).
    [CrossRef] [PubMed]
  7. B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
    [CrossRef]
  8. A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
    [CrossRef]
  9. M. Burton and C. Benning, “Comparison of imaging infrared detection algorithms,” Proc. SPIE 302, 26–32 (1981).
  10. A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
    [CrossRef]
  11. I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).
    [CrossRef]
  12. S. G. Mallat, Wavelet Tour of Signal Processing, 2nd ed.(Academic, 2008).
  13. E. Abdelkawy and D. McGaughy, “Wavelet-based image target detection methods,” Proc. SPIE 5094, 337–347 (2003).
    [CrossRef]
  14. S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
    [CrossRef]
  15. F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
    [CrossRef]
  16. K. Riley and A. J. Devaney,”Wavelet processing of images for target detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).
    [CrossRef]
  17. S. Arivazhagan and L. Ganesan, “Automatic target detection using wavelet transform,” EURASIP J. Appl. Signal Process. 2004, 2663–2674 (2004).
    [CrossRef]
  18. X.-P. Zhang and M. D. Desai, “Segmentation of bright targets using wavelets and adaptive thresholding,” IEEE Trans. Image Process. 10, 1020–1030 (2001).
    [CrossRef]
  19. F. A. Sadjadi, “Infrared target detection with probability density functions of wavelet transform subbands,” Appl. Opt. 43, 315–323 (2004).
    [CrossRef] [PubMed]
  20. R. N. Strickland and H. L. Hahn, “Wavelet transform methods for object detection and recovery,” IEEE Trans. Image Process. 6, 724–735 (1997).
    [CrossRef] [PubMed]
  21. G. Kronquist and H. Storm, “Target detection with local discriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).
    [CrossRef]
  22. X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).
  23. J. D. Barnes, “Multiscale anomaly detection and image registration algorithms for airborne landmine detection.” M.S. thesis (University of Missouri-Rolla, 2006).
  24. J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
    [CrossRef] [PubMed]
  25. K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
    [CrossRef]
  26. M. J. Shensa, “The discrete wavelet transform: wedding the á trous and Mallat algorithms,”IEEE Trans. Signal Process. 40, 2464–2482 (1992).
    [CrossRef]
  27. S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
    [CrossRef]

2004

S. Arivazhagan and L. Ganesan, “Automatic target detection using wavelet transform,” EURASIP J. Appl. Signal Process. 2004, 2663–2674 (2004).
[CrossRef]

F. A. Sadjadi, “Infrared target detection with probability density functions of wavelet transform subbands,” Appl. Opt. 43, 315–323 (2004).
[CrossRef] [PubMed]

2003

E. Abdelkawy and D. McGaughy, “Wavelet-based image target detection methods,” Proc. SPIE 5094, 337–347 (2003).
[CrossRef]

H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
[CrossRef]

2002

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

2001

X.-P. Zhang and M. D. Desai, “Segmentation of bright targets using wavelets and adaptive thresholding,” IEEE Trans. Image Process. 10, 1020–1030 (2001).
[CrossRef]

2000

S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
[CrossRef]

1999

G. Kronquist and H. Storm, “Target detection with local discriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).
[CrossRef]

1997

S. Z. Der and R. Chellappa, “Probe-based automatic target recognition in infrared imagery,” IEEE Trans. Image Process. 6, 92–102 (1997).
[CrossRef] [PubMed]

R. N. Strickland and H. L. Hahn, “Wavelet transform methods for object detection and recovery,” IEEE Trans. Image Process. 6, 724–735 (1997).
[CrossRef] [PubMed]

1996

K. Riley and A. J. Devaney,”Wavelet processing of images for target detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).
[CrossRef]

K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
[CrossRef]

1995

J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

1992

M. J. Shensa, “The discrete wavelet transform: wedding the á trous and Mallat algorithms,”IEEE Trans. Signal Process. 40, 2464–2482 (1992).
[CrossRef]

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

1990

I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).
[CrossRef]

1989

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

1986

B. Bhanu, “Automatic target recognition: state of the art survey,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 364–379 (1986).
[CrossRef]

1985

A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
[CrossRef]

1981

M. Burton and C. Benning, “Comparison of imaging infrared detection algorithms,” Proc. SPIE 302, 26–32 (1981).

Abdelkawy, E.

E. Abdelkawy and D. McGaughy, “Wavelet-based image target detection methods,” Proc. SPIE 5094, 337–347 (2003).
[CrossRef]

Ahmed, F.

F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

Alam, M. S.

F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

Arivazhagan, S.

S. Arivazhagan and L. Ganesan, “Automatic target detection using wavelet transform,” EURASIP J. Appl. Signal Process. 2004, 2663–2674 (2004).
[CrossRef]

Barnes, J. D.

J. D. Barnes, “Multiscale anomaly detection and image registration algorithms for airborne landmine detection.” M.S. thesis (University of Missouri-Rolla, 2006).

Beaven, S. G.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

Belzer, B.

J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Benning, C.

M. Burton and C. Benning, “Comparison of imaging infrared detection algorithms,” Proc. SPIE 302, 26–32 (1981).

Bhanu, B.

B. Bhanu, “Automatic target recognition: state of the art survey,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 364–379 (1986).
[CrossRef]

Burton, M.

M. Burton and C. Benning, “Comparison of imaging infrared detection algorithms,” Proc. SPIE 302, 26–32 (1981).

Chan, A. L.

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
[CrossRef]

Chellappa, R.

S. Z. Der and R. Chellappa, “Probe-based automatic target recognition in infrared imagery,” IEEE Trans. Image Process. 6, 92–102 (1997).
[CrossRef] [PubMed]

S. Kuttikkad and R. Chellappa, “Non-Gaussian CFAR techniques for target detection in high resolution SAR images,” in Proceedings of the International Conference on Image Processing (IEEE, 1994), pp. 910–914.

Der, S. Z.

H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
[CrossRef]

S. Z. Der and R. Chellappa, “Probe-based automatic target recognition in infrared imagery,” IEEE Trans. Image Process. 6, 92–102 (1997).
[CrossRef] [PubMed]

Desai, M. D.

X.-P. Zhang and M. D. Desai, “Segmentation of bright targets using wavelets and adaptive thresholding,” IEEE Trans. Image Process. 10, 1020–1030 (2001).
[CrossRef]

Devaney, A. J.

K. Riley and A. J. Devaney,”Wavelet processing of images for target detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).
[CrossRef]

Gagliardi, R. M.

A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
[CrossRef]

Ganesan, L.

S. Arivazhagan and L. Ganesan, “Automatic target detection using wavelet transform,” EURASIP J. Appl. Signal Process. 2004, 2663–2674 (2004).
[CrossRef]

Hahn, H. L.

R. N. Strickland and H. L. Hahn, “Wavelet transform methods for object detection and recovery,” IEEE Trans. Image Process. 6, 724–735 (1997).
[CrossRef] [PubMed]

Herley, C.

K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
[CrossRef]

Hoff, L. E.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

Juday, R. D.

B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
[CrossRef]

Karim, M. A.

F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

Kraske, W.

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

Kronquist, G.

G. Kronquist and H. Storm, “Target detection with local discriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).
[CrossRef]

Kumar, B. V. K. V.

B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
[CrossRef]

Kuttikkad, S.

S. Kuttikkad and R. Chellappa, “Non-Gaussian CFAR techniques for target detection in high resolution SAR images,” in Proceedings of the International Conference on Image Processing (IEEE, 1994), pp. 910–914.

Kwon, H.

H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
[CrossRef]

Liao, J.

J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Liu, J.

S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
[CrossRef]

Mahalanobis, A.

B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
[CrossRef]

Mallat, S. G.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

S. G. Mallat, Wavelet Tour of Signal Processing, 2nd ed.(Academic, 2008).

Margalit, A.

A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
[CrossRef]

McGaughy, D.

E. Abdelkawy and D. McGaughy, “Wavelet-based image target detection methods,” Proc. SPIE 5094, 337–347 (2003).
[CrossRef]

Nasrabadi, N. M.

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
[CrossRef]

H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
[CrossRef]

Ramchandran, K.

K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
[CrossRef]

Reed, I. S.

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).
[CrossRef]

A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
[CrossRef]

Riley, K.

K. Riley and A. J. Devaney,”Wavelet processing of images for target detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).
[CrossRef]

Sadjadi, F. A.

Schaum, A. P.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

Shensa, M. J.

M. J. Shensa, “The discrete wavelet transform: wedding the á trous and Mallat algorithms,”IEEE Trans. Signal Process. 40, 2464–2482 (1992).
[CrossRef]

Stein, D. W. J.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

Stocker, A. D.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

Storm, H.

G. Kronquist and H. Storm, “Target detection with local discriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).
[CrossRef]

Strickland, R. N.

R. N. Strickland and H. L. Hahn, “Wavelet transform methods for object detection and recovery,” IEEE Trans. Image Process. 6, 724–735 (1997).
[CrossRef] [PubMed]

Vetterli, M.

K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
[CrossRef]

Villasenor, J.

J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

Wen, S.

S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
[CrossRef]

Winter, E. M.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

Yang, J.

S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
[CrossRef]

Yu, X.

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).
[CrossRef]

Zhang, X.-P.

X.-P. Zhang and M. D. Desai, “Segmentation of bright targets using wavelets and adaptive thresholding,” IEEE Trans. Image Process. 10, 1020–1030 (2001).
[CrossRef]

Appl. Opt.

EURASIP J. Appl. Signal Process.

S. Arivazhagan and L. Ganesan, “Automatic target detection using wavelet transform,” EURASIP J. Appl. Signal Process. 2004, 2663–2674 (2004).
[CrossRef]

IEEE Signal Process. Mag.

D. W. J. Stein, S. G. Beaven, L. E. Hoff, E. M. Winter, A. P. Schaum, and A. D. Stocker, “Anomaly detection from hyperspectral imagery,” IEEE Signal Process. Mag. 19, 58–69 (2002).
[CrossRef]

IEEE Trans Image Process.

J. Villasenor, B. Belzer, and J. Liao, “Wavelet filter evaluation for image compression,” IEEE Trans Image Process. 4, 1053–1060 (1995).
[CrossRef] [PubMed]

IEEE Trans. Acoust. Speech Signal Process.

X. Yu, I. S. Reed, W. Kraske, and A. D. Stocker, “A robust adaptive multi-spectral object detection by using wavelet transform,” IEEE Trans. Acoust. Speech Signal Process. 5, 141–144 (1992).

I. S. Reed and X. Yu, “Adaptive multiple-band CFAR detection of an optical pattern with unknown spectral distribution,” IEEE Trans. Acoust. Speech Signal Process. 38, 1760–1770(1990).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

B. Bhanu, “Automatic target recognition: state of the art survey,” IEEE Trans. Aerosp. Electron. Syst. AES-22, 364–379 (1986).
[CrossRef]

A. Margalit, I. S. Reed, and R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. AES-21, 394–405 (1985).
[CrossRef]

IEEE Trans. Image Process.

S. Z. Der and R. Chellappa, “Probe-based automatic target recognition in infrared imagery,” IEEE Trans. Image Process. 6, 92–102 (1997).
[CrossRef] [PubMed]

X.-P. Zhang and M. D. Desai, “Segmentation of bright targets using wavelets and adaptive thresholding,” IEEE Trans. Image Process. 10, 1020–1030 (2001).
[CrossRef]

R. N. Strickland and H. L. Hahn, “Wavelet transform methods for object detection and recovery,” IEEE Trans. Image Process. 6, 724–735 (1997).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell.

S. G. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

IEEE Trans. Signal Process.

M. J. Shensa, “The discrete wavelet transform: wedding the á trous and Mallat algorithms,”IEEE Trans. Signal Process. 40, 2464–2482 (1992).
[CrossRef]

Inf. Fusion

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Dualband FLIR fusion for automatic target recognition,” Inf. Fusion 4, 35–45(2003).
[CrossRef]

Int. J. Imaging Syst. Technol.

K. Riley and A. J. Devaney,”Wavelet processing of images for target detection,” Int. J. Imaging Syst. Technol. 7, 404–420(1996).
[CrossRef]

Opt. Eng.

F. Ahmed, M. A. Karim, and M. S. Alam, “Wavelet transform-based correlator for the recognition of rotationally distorted images,” Opt. Eng. 34, 3187–3192 (1995).
[CrossRef]

H. Kwon, S. Z. Der, and N. M. Nasrabadi, “Adaptive anomaly detection using subspace separation for hyperspectral imagery,” Opt. Eng. 42, 3342–3351 (2003).
[CrossRef]

A. L. Chan, S. Z. Der, and N. M. Nasrabadi, “Multistage infrared target detection,” Opt. Eng. 42, 2746–2754 (2003).
[CrossRef]

Proc. IEEE

K. Ramchandran, M. Vetterli, and C. Herley, “Wavelets, subband coding, and best bases,” Proc. IEEE 84, 541–560(1996).
[CrossRef]

Proc. SPIE

G. Kronquist and H. Storm, “Target detection with local discriminant bases and wavelets,” Proc. SPIE 3710, 675–683(1999).
[CrossRef]

M. Burton and C. Benning, “Comparison of imaging infrared detection algorithms,” Proc. SPIE 302, 26–32 (1981).

E. Abdelkawy and D. McGaughy, “Wavelet-based image target detection methods,” Proc. SPIE 5094, 337–347 (2003).
[CrossRef]

S. Wen, J. Yang, and J. Liu, “Small IR target detection approach based on multiscale relative distance image,” Proc. SPIE 4077, 194–197 (2000).
[CrossRef]

Other

S. G. Mallat, Wavelet Tour of Signal Processing, 2nd ed.(Academic, 2008).

S. Kuttikkad and R. Chellappa, “Non-Gaussian CFAR techniques for target detection in high resolution SAR images,” in Proceedings of the International Conference on Image Processing (IEEE, 1994), pp. 910–914.

B. V. K. V. Kumar, A. Mahalanobis, and R. D. Juday, Correlation Pattern Recognition (Cambridge U. Press, 2005).
[CrossRef]

J. D. Barnes, “Multiscale anomaly detection and image registration algorithms for airborne landmine detection.” M.S. thesis (University of Missouri-Rolla, 2006).

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Figures (15)

Fig. 1
Fig. 1

Wavelet filter bank for one-level image decomposition.

Fig. 2
Fig. 2

Wavelet uniform decomposition of (a) one level and (b) two levels.

Fig. 3
Fig. 3

Uniform three-level wavelet decomposition of (a) LW image and (b) MW image.

Fig. 4
Fig. 4

Sliding dual window: inner window region (IWR) and an outer window region (OWR).

Fig. 5
Fig. 5

Wavelet subband-image cube: B uniform subbands concatenated.

Fig. 6
Fig. 6

Wavelet-RX dual-band output of the four terms in Eq. (8) using LW and MW concatenated wavelet decomposed data: (a) first term, (b) second term, (c) third term, and (d) fourth term.

Fig. 7
Fig. 7

CFAR dual-band outputs of the four terms in Eq. (8) using LW and MW concatenated raw data: (a) first term, (b) second term, (c) third term, and (d) fourth term.

Fig. 8
Fig. 8

Original (a) LW and (b) MW images.

Fig. 9
Fig. 9

CFAR output results from (a) LW, (b) MW, and (c) LW + MW .

Fig. 10
Fig. 10

Wavelet-RX output results from (a) LW, (b) MW, and (c) LW + MW .

Fig. 11
Fig. 11

ROC plots for CFAR applied to LW, MW, and LW + MW .

Fig. 12
Fig. 12

ROC plots for wavelet-RX applied to (a) LW, (b) MW, and (c) LW + MW .

Fig. 13
Fig. 13

ROC plots for LW + MW , LW, and MW separately.

Fig. 14
Fig. 14

ROC plots for CFAR and wavelet-RX using LW and MW.

Fig. 15
Fig. 15

ROC plots for five subbands concatenated versus average and maximum.

Equations (12)

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δ CFAR ( r i j ) = ( r i j μ ) T σ 1 ( r i j μ ) ,
x LW ( i , j ) = ( x 1 ( i , j ) , x 2 ( i , j ) , , x B ( i , j ) ) T ,
X = [ x ( 1 ) , x ( 2 ) , , x ( N ) ] .
δ rx ( r i j ) = ( r i j μ ) T C ^ LW 1 ( r i j μ ) ,
C ^ LW = 1 N ( X X T ) .
x LW MW ( i , j ) = [ x LW ( i , j ) x MW ( i , j ) ] ,
δ rx LW MW ( i , j ) = ( [ x LW ( i , j ) x MW ( i , j ) ] [ μ ^ LW μ ^ MW ] ) T × ( C ^ LW LW C ^ LW MW C ^ MW LW C ^ MW MW ) 1 × ( [ x LW ( i , j ) x MW ( i , j ) ] [ μ ^ LW μ ^ MW ] ) ,
C ^ 1 = [ C ^ LW LW C ^ LW MW C ^ MW LW C ^ MW MW ] 1 = [ Λ ^ LW LW Λ ^ LW MW Λ ^ MW LW Λ ^ MW MW ] .
δ rx LW MW ( i , j ) = ( [ x LW ( i , j ) x MW ( i , j ) ] [ μ ^ LW μ ^ MW ] ) T ( Λ ^ LW LW Λ ^ LW MW Λ ^ MW LW Λ ^ MW MW ) ( [ x LW ( i , j ) x MW ( i , j ) ] [ μ ^ LW μ ^ MW ] ) = ( r LW ( i , j ) μ ^ LW ) T Λ ^ LW LW ( r LW ( i , j ) μ ^ LW ) + ( r LW ( i , j ) μ ^ LW ) T Λ ^ LW MW ( r MW ( i , j ) μ ^ MW ) + ( r MW ( i , j ) μ ^ MW ) T Λ ^ MW LW ( r LW ( i , j ) μ ^ LW ) + ( r MW ( i , j ) μ ^ MW ) T Λ ^ MW MW ( r MW ( i , j ) μ ^ MW ) .
x LW MW ( i , j ) = [ x LW ( i , j ) x MW ( i , j ) ] ,
P d = N hit N t .
P fa = N miss N tot ,

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