Abstract

We introduce a dynamic range image compression technique for nonlinear deconvolution; the impulse response of the distortion function and the noisy distorted image are jointly transformed to pump a clean reference beam in a two-beam coupling arrangement. The Fourier transform of the pumped reference beam contains the deconvolved image and its conjugate. In contrast to standard deconvolution approaches, for which noise can be a limiting factor in the performance, this approach allows the retrieval of distorted signals embedded in a very high-noise environment.

© 2006 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chaps. 4, pp. 213-216 and 6, p. 247.
  2. J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).
  3. J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
    [CrossRef]
  4. J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).
  5. J. Khoury, G. Asimellis, and C. L. Woods, Opt. Lett. 20, 2321 (1995).
    [CrossRef] [PubMed]
  6. G. Asimellis, J. Khoury, and C. L. Woods, J. Opt. Soc. Am. A 13, 1345 (1996). See also Ref. .
    [CrossRef]
  7. G. Asimellis, "Holographic implementation of nonlinear joint-transform correlators," Ph.D. thesis (Tufts University, 1997), Chap. 5.
  8. J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
    [CrossRef]
  9. L. P. Yaroslavsky, Appl. Opt. 31, 1677 (1992).
    [CrossRef] [PubMed]
  10. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, 2002).
  11. B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
    [CrossRef]
  12. M. S. Alam, Opt. Eng. 37, 556 (1998).
    [CrossRef]
  13. M. S. Alam, in Proc. SPIE 3386, 190 (1998).
    [CrossRef]
  14. B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
    [CrossRef]
  15. C. J. Weaver and J. W. Goodman, Appl. Opt. 5, 1248 (1966).
    [CrossRef] [PubMed]
  16. http://www.ctio.noao.edu/~atokovin/tutorial/part5/mcao.html.
  17. J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
    [CrossRef]
  18. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chaps. 12-13, pp. 253-311.

2004 (1)

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

2000 (1)

J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
[CrossRef]

1998 (3)

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

M. S. Alam, Opt. Eng. 37, 556 (1998).
[CrossRef]

M. S. Alam, in Proc. SPIE 3386, 190 (1998).
[CrossRef]

1996 (1)

1995 (1)

1994 (2)

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

1992 (1)

1991 (1)

J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).

1989 (1)

B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
[CrossRef]

1966 (1)

Alam, M. S.

M. S. Alam, Opt. Eng. 37, 556 (1998).
[CrossRef]

M. S. Alam, in Proc. SPIE 3386, 190 (1998).
[CrossRef]

Asimellis, G.

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

G. Asimellis, J. Khoury, and C. L. Woods, J. Opt. Soc. Am. A 13, 1345 (1996). See also Ref. .
[CrossRef]

J. Khoury, G. Asimellis, and C. L. Woods, Opt. Lett. 20, 2321 (1995).
[CrossRef] [PubMed]

G. Asimellis, "Holographic implementation of nonlinear joint-transform correlators," Ph.D. thesis (Tufts University, 1997), Chap. 5.

Bennet, W.

M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chaps. 4, pp. 213-216 and 6, p. 247.

Caulfield, H. J.

B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
[CrossRef]

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chaps. 12-13, pp. 253-311.

Fu, J.

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

Gianino, P. D.

J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

Golomb, M. C.

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).

Gonzalez, R. C.

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

Goodhue, W.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Goodman, J. W.

Haji-Saeed, B.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Horner, J. L.

B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
[CrossRef]

Javidi, B.

B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
[CrossRef]

Khoury, J.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

G. Asimellis, J. Khoury, and C. L. Woods, J. Opt. Soc. Am. A 13, 1345 (1996). See also Ref. .
[CrossRef]

J. Khoury, G. Asimellis, and C. L. Woods, Opt. Lett. 20, 2321 (1995).
[CrossRef] [PubMed]

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).

Kierstead, J.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Leon, R.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Pyburn, D.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chaps. 12-13, pp. 253-311.

Schwartz, M.

M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chaps. 4, pp. 213-216 and 6, p. 247.

Sengupta, S. K.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Stein, S.

M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chaps. 4, pp. 213-216 and 6, p. 247.

Testorf, M.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

Weaver, C. J.

Woods, C. L.

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

G. Asimellis, J. Khoury, and C. L. Woods, J. Opt. Soc. Am. A 13, 1345 (1996). See also Ref. .
[CrossRef]

J. Khoury, G. Asimellis, and C. L. Woods, Opt. Lett. 20, 2321 (1995).
[CrossRef] [PubMed]

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).

Woods, R. E.

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

Yaroslavsky, L. P.

Appl. Opt. (2)

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

G. Asimellis, J. Khoury, and C. L. Woods, J. Opt. Soc. Am. A 13, 1345 (1996). See also Ref. .
[CrossRef]

J. Khoury, J. Fu, M. C. Golomb, and C. L. Woods, J. Opt. Soc. Am. A 11, 1960 (1994).
[CrossRef]

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

J. Khoury, M. C. Golomb, P. D. Gianino, and C. L. Woods, J. Opt. Soc. Am. B 167, 11 (1994).

Opt. Commun. (1)

B. Javidi, J. L. Horner and H. J. Caulfield, Opt. Commun. 70, 369 (1989).
[CrossRef]

Opt. Eng. (4)

B. Haji-Saeed, D. Pyburn, R. Leon, S. K. Sengupta, W. Goodhue, M. Testorf, J. Kierstead, J. Khoury, and C. L. Woods, Opt. Eng. 43, 1862 (2004).
[CrossRef]

M. S. Alam, Opt. Eng. 37, 556 (1998).
[CrossRef]

J. Khoury, G. Asimellis, P. D. Gianino, and C. L. Woods, Opt. Eng. 37, 66 (1998).
[CrossRef]

J. Khoury, P. D. Gianino, and C. L. Woods, Opt. Eng. 39, 1177 (2000).
[CrossRef]

Opt. Lett. (2)

J. Khoury, G. Asimellis, and C. L. Woods, Opt. Lett. 20, 2321 (1995).
[CrossRef] [PubMed]

J. Khoury, M. C. Golomb, and C. L. Woods, Opt. Lett. 16, 749 (1991).

Proc. SPIE (1)

M. S. Alam, in Proc. SPIE 3386, 190 (1998).
[CrossRef]

Other (5)

G. Asimellis, "Holographic implementation of nonlinear joint-transform correlators," Ph.D. thesis (Tufts University, 1997), Chap. 5.

M. Schwartz, W. Bennet, and S. Stein, Communication Systems and Techniques (McGraw-Hill, 1966), Chaps. 4, pp. 213-216 and 6, p. 247.

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

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signal and Noise (McGraw-Hill, 1958), Chaps. 12-13, pp. 253-311.

http://www.ctio.noao.edu/~atokovin/tutorial/part5/mcao.html.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic diagram illustrating nonlinear deconvolution via photorefractive two-beam coupling.

Fig. 2
Fig. 2

Computer simulation of image deconvolution via two-beam coupling in the linear range: A, Joint image of the input and the point source. B, Output joint image, which consists of a distorted noisy input and the impulse response of the distortion medium (atmospheric turbulence). C, Corrected image in the linear range.

Fig. 3
Fig. 3

Computer simulation illustration of nonlinear deconvolution by photorefractive two-beam coupling: A, B, and C, distorted images with additive low-frequency noise by use of motion, phase only, and misfocusing aberration functions, respectively. A , B , and C , respectively, show the corrected versions, of A, B, and C.

Equations (5)

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

A 3 = A 2 2 H + H F 2 A 1 A 2 2 H + H F 2 + A 1 2 = m H + H F 2 A 1 m H + H F 2 + 1 ,
A 3 = m H + H F 2 A 1 = m ( H 2 + H F 2 + F H H * + F * H H * ) A 1 ,
A 3 = m H + H F 2 A 1 = m ( 1 + F 2 + F + F * ) .
A 3 = H k ( ν x , ν y ) cos ( 2 k y o v y + k ϕ F ) ,
H k ( v x , v y ) = ( 1 ) k { [ 1 + m ( H H F ) 2 ] [ 1 + m ( H + H F 2 ) ] } 1 2 ( 2 m H H F 1 + m ( H 2 + H 2 F 2 ) + { [ 1 + m ( H H F 2 ) ] [ 1 + m ( H + H F 2 ) ] } 1 2 ) k .

Metrics