Abstract

Synthetic radar image recognition is an area of interest for military applications including automatic target recognition, air traffic control, and remote sensing. Here a dynamic range compression two-beam-coupling joint transform correlator for detecting synthetic aperture radar targets is utilized. The joint input image consists of a prepower-law, enhanced scattering center of the input image and a linearly synthesized power-law-enhanced scattering center template. Enhancing the scattering center of both the synthetic template and the input image furnishes the conditions for achieving dynamic range compression correlation in two-beam coupling. Dynamic range compression (a) enhances the signal-to-noise ratio, (b) enhances the high frequencies relative to low frequencies, and (c) converts the noise to high frequency components. This improves the correlation-peak intensity to the mean of the surrounding noise significantly. Dynamic range compression correlation has already been demonstrated to outperform many optimal correlation filters in detecting signals in severe noise environments. The performance is evaluated via established metrics such as peak-to-correlation energy, Horner efficiency, and correlation-peak intensity. The results showed significant improvement as the power increased.

© 2008 Optical Society of America

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References

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  1. B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architecture and Applications (Oxford U. Press, 1998), Chap. 11, pp. 281-311.
  2. R. Shenoy and D. P. Casasent, “Multiclass SAR feature space trajectory FST neural net class and pose estimation results,” Proc. SPIE 3070, 121-124 (1997).
    [CrossRef]
  3. R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).
  4. S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
    [CrossRef]
  5. M. Boshra and B. Bhanu, “Performance modeling of feature-based classification in SAR imagery,” Proc. SPIE 3370, 661-674 (1998).
    [CrossRef]
  6. D. K. Barton, Modern Radar Systems Analysis (Artech House, 1988), p. 209.
  7. H. Urkowitz, Modern Radar Analysis Evaluation and System Design, R. S. Berkowitz, ed. (Wiley, 1965), Chap. 1, pp. 197-215.
  8. J. Khoury, P. D. Gianino, and C. L. Woods, “Synthetic aperture radar image correlation by use of preprocessing for enhancement of scattering centers,” Opt. Lett. 25, 1544-1546 (2000).
    [CrossRef]
  9. J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
    [CrossRef]
  10. J. L. Horner and P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812-816 (1984).
    [CrossRef] [PubMed]
  11. J. L. Horner and J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609-611 (1985).
    [CrossRef] [PubMed]
  12. J. Khoury, J. Fu, M. Cronin-Golomb, and C. Woods, “Quadratic processing and nonlinear optical phase rectification in noise reduction,” J. Opt. Soc. Am. B 11, 1960-1971 (1994).
    [CrossRef]
  13. J. Khoury, M. Cronin-Golomb, P. Gianino, and C. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B 11, 2167-2174 (1994).
    [CrossRef]
  14. G. Asimellis, J. Khoury, and C. Woods, “Effects of saturation on the nonlinear incoherent-erasure joint-transform correlator,” J. Opt. Soc. Am. A 13, 1345-1356 (1996).
    [CrossRef]
  15. J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
    [CrossRef]
  16. M. S. Alam and J. S. Khoury, “Fringe-adjusted incoherent erasure joint transform correlator,” Opt. Eng. 37, 75-82 (1998).
    [CrossRef]
  17. B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
    [CrossRef]
  18. B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
    [CrossRef] [PubMed]
  19. B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).
  20. D. Casasent and S. Ashizawa, “Synthetic aperture radar detection, recognition and clutter rejection with minimum noise and correlation energy filters,” Opt. Eng. 36, 2729-2736(1997).
    [CrossRef]
  21. R. Shenoy and D. Casasent, “Eigen-MINACE detection filter with improved capacity,” Proc. SPIE 3370, 435-447 (1998).
    [CrossRef]
  22. J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice-Hall, 2002).
  23. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chap. 12-13, pp. 255-311.
  24. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).
  25. http://hyperphysics.phy-astr.gsu.edu/hbase/audio/tape4.html#c2.

2007 (1)

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

2006 (1)

2001 (1)

J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
[CrossRef]

2000 (1)

1998 (5)

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

M. S. Alam and J. S. Khoury, “Fringe-adjusted incoherent erasure joint transform correlator,” Opt. Eng. 37, 75-82 (1998).
[CrossRef]

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

M. Boshra and B. Bhanu, “Performance modeling of feature-based classification in SAR imagery,” Proc. SPIE 3370, 661-674 (1998).
[CrossRef]

R. Shenoy and D. Casasent, “Eigen-MINACE detection filter with improved capacity,” Proc. SPIE 3370, 435-447 (1998).
[CrossRef]

1997 (2)

D. Casasent and S. Ashizawa, “Synthetic aperture radar detection, recognition and clutter rejection with minimum noise and correlation energy filters,” Opt. Eng. 36, 2729-2736(1997).
[CrossRef]

R. Shenoy and D. P. Casasent, “Multiclass SAR feature space trajectory FST neural net class and pose estimation results,” Proc. SPIE 3070, 121-124 (1997).
[CrossRef]

1996 (1)

1994 (2)

1985 (1)

1984 (1)

Alam, M. S.

M. S. Alam and J. S. Khoury, “Fringe-adjusted incoherent erasure joint transform correlator,” Opt. Eng. 37, 75-82 (1998).
[CrossRef]

Ashizawa, S.

D. Casasent and S. Ashizawa, “Synthetic aperture radar detection, recognition and clutter rejection with minimum noise and correlation energy filters,” Opt. Eng. 36, 2729-2736(1997).
[CrossRef]

Asimellis, G.

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

G. Asimellis, J. Khoury, and C. Woods, “Effects of saturation on the nonlinear incoherent-erasure joint-transform correlator,” J. Opt. Soc. Am. A 13, 1345-1356 (1996).
[CrossRef]

Barton, D. K.

D. K. Barton, Modern Radar Systems Analysis (Artech House, 1988), p. 209.

Bhanu, B.

M. Boshra and B. Bhanu, “Performance modeling of feature-based classification in SAR imagery,” Proc. SPIE 3370, 661-674 (1998).
[CrossRef]

Boone, B. G.

B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architecture and Applications (Oxford U. Press, 1998), Chap. 11, pp. 281-311.

Boshra, M.

M. Boshra and B. Bhanu, “Performance modeling of feature-based classification in SAR imagery,” Proc. SPIE 3370, 661-674 (1998).
[CrossRef]

Casasent, D.

R. Shenoy and D. Casasent, “Eigen-MINACE detection filter with improved capacity,” Proc. SPIE 3370, 435-447 (1998).
[CrossRef]

D. Casasent and S. Ashizawa, “Synthetic aperture radar detection, recognition and clutter rejection with minimum noise and correlation energy filters,” Opt. Eng. 36, 2729-2736(1997).
[CrossRef]

Casasent, D. P.

R. Shenoy and D. P. Casasent, “Multiclass SAR feature space trajectory FST neural net class and pose estimation results,” Proc. SPIE 3070, 121-124 (1997).
[CrossRef]

Cronin-Golomb, M.

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chap. 12-13, pp. 255-311.

Fu, J.

Gianino, P.

Gianino, P. D.

J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, “Synthetic aperture radar image correlation by use of preprocessing for enhancement of scattering centers,” Opt. Lett. 25, 1544-1546 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

J. L. Horner and P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812-816 (1984).
[CrossRef] [PubMed]

Gonzalez, R. C.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).

Goodhue, W.

Goodhue, W. D.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

Haji-saeed, B.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
[CrossRef] [PubMed]

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

Horner, J. L.

Johnson, D.

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

Kaplan, L. M.

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

Keydel, E.

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

Khoury, J.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
[CrossRef] [PubMed]

J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, “Synthetic aperture radar image correlation by use of preprocessing for enhancement of scattering centers,” Opt. Lett. 25, 1544-1546 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

G. Asimellis, J. Khoury, and C. Woods, “Effects of saturation on the nonlinear incoherent-erasure joint-transform correlator,” J. Opt. Soc. Am. A 13, 1345-1356 (1996).
[CrossRef]

J. Khoury, M. Cronin-Golomb, P. Gianino, and C. Woods, “Photorefractive two-beam coupling nonlinear joint transform correlator,” J. Opt. Soc. Am. B 11, 2167-2174 (1994).
[CrossRef]

J. Khoury, J. Fu, M. Cronin-Golomb, and C. Woods, “Quadratic processing and nonlinear optical phase rectification in noise reduction,” J. Opt. Soc. Am. B 11, 1960-1971 (1994).
[CrossRef]

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

Khoury, J. S.

M. S. Alam and J. S. Khoury, “Fringe-adjusted incoherent erasure joint transform correlator,” Opt. Eng. 37, 75-82 (1998).
[CrossRef]

Kierstead, J.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
[CrossRef] [PubMed]

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

Leger, J. R.

Murenzi, R.

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

Namuduri, K. R.

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

Proakis, J. G.

J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice-Hall, 2002).

Rajilic, V.

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chap. 12-13, pp. 255-311.

Salehi, M.

J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice-Hall, 2002).

Semwogerere, D.

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

Sengupta, S. K.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
[CrossRef] [PubMed]

Shenoy, R.

R. Shenoy and D. Casasent, “Eigen-MINACE detection filter with improved capacity,” Proc. SPIE 3370, 435-447 (1998).
[CrossRef]

R. Shenoy and D. P. Casasent, “Multiclass SAR feature space trajectory FST neural net class and pose estimation results,” Proc. SPIE 3070, 121-124 (1997).
[CrossRef]

Sieron, R.

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

Stanhope, S. A.

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

Urkowitz, H.

H. Urkowitz, Modern Radar Analysis Evaluation and System Design, R. S. Berkowitz, ed. (Wiley, 1965), Chap. 1, pp. 197-215.

Williams, W.

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

Woods, C.

Woods, C. L.

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

B. Haji-saeed, S. K. Sengupta, W. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Nonlinear dynamic range compression deconvolution,” Opt. Lett. 31, 1969-1971 (2006).
[CrossRef] [PubMed]

J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, “Synthetic aperture radar image correlation by use of preprocessing for enhancement of scattering centers,” Opt. Lett. 25, 1544-1546 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

Woods, R. E.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).

Appl. Opt. (2)

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (2)

Opt. Eng. (4)

D. Casasent and S. Ashizawa, “Synthetic aperture radar detection, recognition and clutter rejection with minimum noise and correlation energy filters,” Opt. Eng. 36, 2729-2736(1997).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, “Optimal synthetic aperture radar image correlation using enhanced scattering centers in holographic data storage,” Opt. Eng. 40, 2624-2637 (2001).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, “Nonlinear compansive noise reduction in joint transform correlators,” Opt. Eng. 37, 66-74 (1998).
[CrossRef]

M. S. Alam and J. S. Khoury, “Fringe-adjusted incoherent erasure joint transform correlator,” Opt. Eng. 37, 75-82 (1998).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (5)

B. Haji-saeed, S. K. Sengupta, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution using A-law and μ-law algorithms,” Proc. SPIE 65740, 65740D (2007).
[CrossRef]

S. A. Stanhope, E. Keydel, W. Williams, V. Rajilic, and R. Sieron, “The use of the mean squared error matching metric in a model based automatic target recognition system,” Proc. SPIE 3370, 360-368 (1998).
[CrossRef]

M. Boshra and B. Bhanu, “Performance modeling of feature-based classification in SAR imagery,” Proc. SPIE 3370, 661-674 (1998).
[CrossRef]

R. Shenoy and D. Casasent, “Eigen-MINACE detection filter with improved capacity,” Proc. SPIE 3370, 435-447 (1998).
[CrossRef]

R. Shenoy and D. P. Casasent, “Multiclass SAR feature space trajectory FST neural net class and pose estimation results,” Proc. SPIE 3070, 121-124 (1997).
[CrossRef]

Other (9)

R. Murenzi, D. Semwogerere, D. Johnson, L. M. Kaplan, and K. R. Namuduri, “Detection/recognition of targets in low-resolution FLIR images using 2D directional wavelets,” SPIE Automatic Target Recognition VIII AeroSense Conference(1998).

J. G. Proakis and M. Salehi, Communication Systems Engineering (Prentice-Hall, 2002).

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chap. 12-13, pp. 255-311.

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).

http://hyperphysics.phy-astr.gsu.edu/hbase/audio/tape4.html#c2.

D. K. Barton, Modern Radar Systems Analysis (Artech House, 1988), p. 209.

H. Urkowitz, Modern Radar Analysis Evaluation and System Design, R. S. Berkowitz, ed. (Wiley, 1965), Chap. 1, pp. 197-215.

B. Haji-saeed, W. D. Goodhue, J. Khoury, C. L. Woods, and J. Kierstead, “Dynamic range compression deconvolution,” in Frontiers in Optics (Optical Society of America, 2007).

B. G. Boone, Signal Processing Using Optics: Fundamentals, Devices, Architecture and Applications (Oxford U. Press, 1998), Chap. 11, pp. 281-311.

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Figures (8)

Fig. 1
Fig. 1

Two-beam-coupling joint Fourier processor.

Fig. 2
Fig. 2

A, Intensity of the output beam as a function the beam ratio for different coupling coefficients. B, Grating efficiency as a function of beam ratio for different coupling coefficients.

Fig. 3
Fig. 3

A, E, I, M, Power-law-enhanced scattering images of the SAR image HB03333 extracted from the ROI (MSTAR/15-DEG/COL1/SCENE1/BTR-60). The power-law enhancements for the first column are 1, 2, 4, and 6, respectively. B, F, J, N, Their respective Fourier transforms. C, G, K, O, Their dynamic range compressed Fourier transforms with different beam compression values. The beam ratios for C, G, K, and O are m = 10 7 , m = 10 11 , m = 10 20 and m = 10 29 , respectively. D, H, L, P, The respective enhanced scattering center images after applying dynamic range compression, with a beam ratio of 10 7 on the Fourier spectra in the second column.

Fig. 4
Fig. 4

Enhanced SAR images. A, C, E, G, The power-law enhancement of d images with the power-law of 1, 2, 4, and 6, respectively. B, D, F, H, The simultaneous application of two-beam-coupling dynamic range at beam ratio m = 10 7 and the power-law enhancements of 1, 2, 4, and 6, respectively.

Fig. 5
Fig. 5

A–D, Joint image of power-law-enhanced SAR image and syntactic template extracted from ROI. The power-law enhancements are of 1, 2, 4, and 6, respectively.

Fig. 6
Fig. 6

Two-beam-coupling joint transform correlation results of the inputs from Fig. 3 at a beam ratio of m = 10 7 .

Fig. 7
Fig. 7

Joint transform correlation results with a power-law enhancement of 6 and a dynamic range compression for beam ratio m = 10 7 : A, for in-class target (MSTAR/15-DEG/COL1/SCENE1/BTR-60/HB03341) and B, for out-of-class target (MSTAR/45_DEG/COL2/SCENE1/2S1/HB16946).

Fig. 8
Fig. 8

A, Plots of correlation-peak-intensity, I p ; C, PCE; E, the Horner efficiency as a function of the beam ratio for power-law enhancement of light blue, green, red, and blue; B, correlation-peak-intensity, I p ; D, PCE; and F, the Horner efficiency versus the power-law enhancement where the beam ratio has been taken as a parameter. The beam-ratio parameters for red, blue, green, light blue, and pink are 10 9 , 10 8 , 10 7 , 10 6 , and 10 5 , respectively.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

A ( ν x , ν y ) = A ( 0 ) [ 1 + m / ( λ f l ) 2 | R ( ν x , ν y ) + S ( ν x , ν y ) | 2 1 + m / ( λ f l ) 2 | R ( ν x , ν y ) + S ( ν x , ν y ) | 2 exp ( - Γ l ) ] 1 / 2 ,
A ( ν x , ν y ) = A ( 0 ) - ( Γ l ) m / ( λ f l ) 2 | R ( ν x , ν y ) + S ( ν x , ν y ) | 2 1 + m / ( λ f l ) 2 | R ( ν x , ν y ) + S ( ν x , ν y ) | 2 .
η t ( z ) = | A 2 ( z ) | 2 | A 1 ( 0 ) | 2 = sin 2 [ u ( m , Γ z ) ] ,
u ( m , Γ z ) = { 2 m [ 1 + cosh ( m - 1 ) ] ( 1 + m ) 2 } 1 / 2 × [ tan - 1 exp ( Γ z 2 + 1 2 m ) - tan - 1 exp ( 1 2 m ) ] ,

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