Abstract

The resolution of images acquired by a digital camera is limited to the camera’s sampling interval. The images’ visual quality is affected by the level of the degradations caused by the imaging process from acquisition to display, including quantization, coding, transmission, and digital filtering. The information metric is presented as a design and an assessment tool for high-resolution digital imaging systems and all their subsystems. It associates gains in the acquired information with improvements in resolution, sharpness, and clarity of the final image representation. It demonstrates the need to integrate a digital filtering module that accounts for the optoelectronic imaging degradations in the optoelectronic imaging design and assessment. It further demonstrates the metric’s sensitivity by the assessment of the combined imaging processes as a unified system.

© 2000 Optical Society of America

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References

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  1. H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).
  2. A. K. Jain, Fundamentals of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).
  3. W. F. Schrieber, Fundamental of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).
    [CrossRef]
  4. C. E. Shannon, “Communications in the presence of noise,” Proc. IRE 37, 10–21 (1949).
    [CrossRef]
  5. C. L. Fales, F. O. Huck, “An information theory of image gathering,” Inf. Sci. J. 57–58, 245–285 (1991).
  6. R. Alter-Gartenberg, “Optimal visual communication channels,” IEEE Trans. Commun. 43, 1075–1088 (1995).
    [CrossRef]
  7. C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
    [CrossRef]
  8. F. O. Huck, C. L. Fales, Z. Rahman, Visual Communication: An Information Theory Approach (Kluwer, Boston, 1997).
  9. R. Alter-Gartenberg, S. K. Park, “Information as a quality right for high-resolution imaging,” in Very High Resolution and Quality Imaging III, V. Algazi, A. G. Tescher, eds., Proc. SPIE3308, 16–27 (1998).
    [CrossRef]
  10. F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
    [CrossRef]
  11. S. K. Park, R. Hazra, “Aliasing right noise: a quantitative and qualitative assessment,” in Visual Information Processing ’93, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 2–13 (1993).
  12. S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
    [CrossRef]
  13. J. Olives, B. Lamiscarre, M. Gazalet, “Optimization of electro-optical systems with an image quality right,” in Very High Resolution and Quality Imaging, V. Algazi, S. Ono, A. G. Tescher, eds., Proc. SPIE3025, 158–167 (1997).
  14. R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
    [CrossRef]
  15. R. Alter-Gartenberg, “Multiresolution imaging: an end-to-end assessment,” J. Math. Imag. Vision 8, 59–77 (1998).
    [CrossRef]
  16. R. Alter-Gartenberg, S. K. Park, “Image decomposition: an end-to-end theory,” in Proceedings of the 1997 International Workshop on Sampling Theory and Applications, SAMPTA’97 (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 49–54.
  17. R. Alter-Gartenberg, S. K. Park, “Information efficient decomposition,” in Visual Communications and Image Processing ’98, S. A. Rajala, M. Rabbani, eds., Proc. SPIE3309, 645–654 (1998).
    [CrossRef]
  18. Z. Rahman, R. Alter-Gartenberg, S. E. Reichenbach, “Discrete cosine transform coding: information efficiency and fidelity,” in Visual Information Processing, F. O. Huck, R. D. Juday, eds., Proc. SPIE1705, 145–154 (1993).
  19. Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
    [CrossRef]
  20. R. Alter-Gartenberg, “Efficient visual communication channels,” J. Math. Imag. Vision 5, 1–18 (1995).
    [CrossRef]
  21. R. Alter-Gartenberg, “Nonlinear dynamic range transformation in visual communication channels,” IEEE Trans. Image Process. 5, 538–546 (1996).
    [CrossRef] [PubMed]
  22. F. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
    [CrossRef]
  23. R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.
  24. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).
  25. S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
    [CrossRef]

2000 (1)

1999 (2)

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

1998 (1)

R. Alter-Gartenberg, “Multiresolution imaging: an end-to-end assessment,” J. Math. Imag. Vision 8, 59–77 (1998).
[CrossRef]

1997 (1)

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

1996 (1)

R. Alter-Gartenberg, “Nonlinear dynamic range transformation in visual communication channels,” IEEE Trans. Image Process. 5, 538–546 (1996).
[CrossRef] [PubMed]

1995 (2)

R. Alter-Gartenberg, “Optimal visual communication channels,” IEEE Trans. Commun. 43, 1075–1088 (1995).
[CrossRef]

R. Alter-Gartenberg, “Efficient visual communication channels,” J. Math. Imag. Vision 5, 1–18 (1995).
[CrossRef]

1992 (1)

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

1991 (2)

C. L. Fales, F. O. Huck, “An information theory of image gathering,” Inf. Sci. J. 57–58, 245–285 (1991).

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

1949 (1)

C. E. Shannon, “Communications in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Alter-Gartenberg, R.

F. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

R. Alter-Gartenberg, “Multiresolution imaging: an end-to-end assessment,” J. Math. Imag. Vision 8, 59–77 (1998).
[CrossRef]

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

R. Alter-Gartenberg, “Nonlinear dynamic range transformation in visual communication channels,” IEEE Trans. Image Process. 5, 538–546 (1996).
[CrossRef] [PubMed]

R. Alter-Gartenberg, “Efficient visual communication channels,” J. Math. Imag. Vision 5, 1–18 (1995).
[CrossRef]

R. Alter-Gartenberg, “Optimal visual communication channels,” IEEE Trans. Commun. 43, 1075–1088 (1995).
[CrossRef]

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

R. Alter-Gartenberg, S. K. Park, “Image decomposition: an end-to-end theory,” in Proceedings of the 1997 International Workshop on Sampling Theory and Applications, SAMPTA’97 (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 49–54.

R. Alter-Gartenberg, S. K. Park, “Information efficient decomposition,” in Visual Communications and Image Processing ’98, S. A. Rajala, M. Rabbani, eds., Proc. SPIE3309, 645–654 (1998).
[CrossRef]

R. Alter-Gartenberg, S. K. Park, “Information as a quality right for high-resolution imaging,” in Very High Resolution and Quality Imaging III, V. Algazi, A. G. Tescher, eds., Proc. SPIE3308, 16–27 (1998).
[CrossRef]

R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.

Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
[CrossRef]

Z. Rahman, R. Alter-Gartenberg, S. E. Reichenbach, “Discrete cosine transform coding: information efficiency and fidelity,” in Visual Information Processing, F. O. Huck, R. D. Juday, eds., Proc. SPIE1705, 145–154 (1993).

Andrews, H. C.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).

Davis, R. E.

Fales, C. L.

F. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

C. L. Fales, F. O. Huck, “An information theory of image gathering,” Inf. Sci. J. 57–58, 245–285 (1991).

F. O. Huck, C. L. Fales, Z. Rahman, Visual Communication: An Information Theory Approach (Kluwer, Boston, 1997).

R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.

Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
[CrossRef]

Gazalet, M.

J. Olives, B. Lamiscarre, M. Gazalet, “Optimization of electro-optical systems with an image quality right,” in Very High Resolution and Quality Imaging, V. Algazi, S. Ono, A. G. Tescher, eds., Proc. SPIE3025, 158–167 (1997).

Hazra, R.

S. K. Park, R. Hazra, “Aliasing right noise: a quantitative and qualitative assessment,” in Visual Information Processing ’93, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 2–13 (1993).

Huck, F. O.

F. O. Huck, C. L. Fales, R. E. Davis, R. Alter-Gartenberg, “Visual communication with retinex coding,” Appl. Opt. 39, 1711–1730 (2000).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

C. L. Fales, F. O. Huck, “An information theory of image gathering,” Inf. Sci. J. 57–58, 245–285 (1991).

F. O. Huck, C. L. Fales, Z. Rahman, Visual Communication: An Information Theory Approach (Kluwer, Boston, 1997).

Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
[CrossRef]

R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.

Hunt, B. R.

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

Jain, A. K.

A. K. Jain, Fundamentals of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).

Lamiscarre, B.

J. Olives, B. Lamiscarre, M. Gazalet, “Optimization of electro-optical systems with an image quality right,” in Very High Resolution and Quality Imaging, V. Algazi, S. Ono, A. G. Tescher, eds., Proc. SPIE3025, 158–167 (1997).

McCormick, J. A.

R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.

Narayanswamy, R.

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Olives, J.

J. Olives, B. Lamiscarre, M. Gazalet, “Optimization of electro-optical systems with an image quality right,” in Very High Resolution and Quality Imaging, V. Algazi, S. Ono, A. G. Tescher, eds., Proc. SPIE3025, 158–167 (1997).

Park, S. K.

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

S. K. Park, R. Hazra, “Aliasing right noise: a quantitative and qualitative assessment,” in Visual Information Processing ’93, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 2–13 (1993).

R. Alter-Gartenberg, S. K. Park, “Information efficient decomposition,” in Visual Communications and Image Processing ’98, S. A. Rajala, M. Rabbani, eds., Proc. SPIE3309, 645–654 (1998).
[CrossRef]

R. Alter-Gartenberg, S. K. Park, “Image decomposition: an end-to-end theory,” in Proceedings of the 1997 International Workshop on Sampling Theory and Applications, SAMPTA’97 (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 49–54.

R. Alter-Gartenberg, S. K. Park, “Information as a quality right for high-resolution imaging,” in Very High Resolution and Quality Imaging III, V. Algazi, A. G. Tescher, eds., Proc. SPIE3308, 16–27 (1998).
[CrossRef]

Rahman, Z.

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

Z. Rahman, R. Alter-Gartenberg, S. E. Reichenbach, “Discrete cosine transform coding: information efficiency and fidelity,” in Visual Information Processing, F. O. Huck, R. D. Juday, eds., Proc. SPIE1705, 145–154 (1993).

F. O. Huck, C. L. Fales, Z. Rahman, Visual Communication: An Information Theory Approach (Kluwer, Boston, 1997).

Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
[CrossRef]

Reichenbach, S. E.

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

Z. Rahman, R. Alter-Gartenberg, S. E. Reichenbach, “Discrete cosine transform coding: information efficiency and fidelity,” in Visual Information Processing, F. O. Huck, R. D. Juday, eds., Proc. SPIE1705, 145–154 (1993).

Schrieber, W. F.

W. F. Schrieber, Fundamental of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).
[CrossRef]

Shannon, C. E.

C. E. Shannon, “Communications in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Commun. (1)

R. Alter-Gartenberg, “Optimal visual communication channels,” IEEE Trans. Commun. 43, 1075–1088 (1995).
[CrossRef]

IEEE Trans. Image Process. (1)

R. Alter-Gartenberg, “Nonlinear dynamic range transformation in visual communication channels,” IEEE Trans. Image Process. 5, 538–546 (1996).
[CrossRef] [PubMed]

Inf. Sci. J. (1)

C. L. Fales, F. O. Huck, “An information theory of image gathering,” Inf. Sci. J. 57–58, 245–285 (1991).

J. Math. Imag. Vision (2)

R. Alter-Gartenberg, “Multiresolution imaging: an end-to-end assessment,” J. Math. Imag. Vision 8, 59–77 (1998).
[CrossRef]

R. Alter-Gartenberg, “Efficient visual communication channels,” J. Math. Imag. Vision 5, 1–18 (1995).
[CrossRef]

Multidimen. Sys. Signal Process. (1)

R. Alter-Gartenberg, F. O. Huck, C. L. Fales, Z. Rahman, S. E. Reichenbach, “Multiresponse imaging: information and fidelity,” Multidimen. Sys. Signal Process. 3, 189–210 (1992).
[CrossRef]

Opt. Eng. (3)

S. E. Reichenbach, S. K. Park, R. Narayanswamy, “Characterizing digital image acquisition devices,” Opt. Eng. 30, 170–177 (1991).
[CrossRef]

F. O. Huck, C. L. Fales, R. Alter-Gartenberg, S. K. Park, Z. Rahman, “Information-theoretic assessment of sampled imaging systems,” Opt. Eng. 38, 742–762 (1999).
[CrossRef]

S. K. Park, Z. Rahman, “Fidelity analysis of sampled imaging systems,” Opt. Eng. 38, 786–800 (1999).
[CrossRef]

Philos. Trans. R. Soc. A (1)

C. L. Fales, F. O. Huck, R. Alter-Gartenberg, Z. Rahman, “Image gathering and digital restoration,” Philos. Trans. R. Soc. A 354, 2249–2287 (1997).
[CrossRef]

Proc. IRE (1)

C. E. Shannon, “Communications in the presence of noise,” Proc. IRE 37, 10–21 (1949).
[CrossRef]

Other (13)

H. C. Andrews, B. R. Hunt, Digital Image Restoration (Prentice-Hall, Englewood Cliffs, N.J., 1977).

A. K. Jain, Fundamentals of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).

W. F. Schrieber, Fundamental of Electronic Imaging Systems: Some Aspects of Image Processing (Springer-Verlag, Berlin, 1986).
[CrossRef]

F. O. Huck, C. L. Fales, Z. Rahman, Visual Communication: An Information Theory Approach (Kluwer, Boston, 1997).

R. Alter-Gartenberg, S. K. Park, “Information as a quality right for high-resolution imaging,” in Very High Resolution and Quality Imaging III, V. Algazi, A. G. Tescher, eds., Proc. SPIE3308, 16–27 (1998).
[CrossRef]

J. Olives, B. Lamiscarre, M. Gazalet, “Optimization of electro-optical systems with an image quality right,” in Very High Resolution and Quality Imaging, V. Algazi, S. Ono, A. G. Tescher, eds., Proc. SPIE3025, 158–167 (1997).

S. K. Park, R. Hazra, “Aliasing right noise: a quantitative and qualitative assessment,” in Visual Information Processing ’93, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 2–13 (1993).

R. Alter-Gartenberg, S. K. Park, “Image decomposition: an end-to-end theory,” in Proceedings of the 1997 International Workshop on Sampling Theory and Applications, SAMPTA’97 (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 49–54.

R. Alter-Gartenberg, S. K. Park, “Information efficient decomposition,” in Visual Communications and Image Processing ’98, S. A. Rajala, M. Rabbani, eds., Proc. SPIE3309, 645–654 (1998).
[CrossRef]

Z. Rahman, R. Alter-Gartenberg, S. E. Reichenbach, “Discrete cosine transform coding: information efficiency and fidelity,” in Visual Information Processing, F. O. Huck, R. D. Juday, eds., Proc. SPIE1705, 145–154 (1993).

Z. Rahman, R. Alter-Gartenberg, C. L. Fales, F. O. Huck, “Redundancy reduction in image coding,” in Visual Information Processing II, F. O. Huck, R. D. Juday, eds., Proc. SPIE1961, 102–112 (1993).
[CrossRef]

R. Alter-Gartenberg, C. L. Fales, F. O. Huck, J. A. McCormick, “Image gathering and processing for high-resolution edge detection,” in Progress in Computer Vision and Image Processing, L. Shapiro, A. Rosenfeld, eds. (Academic, New York, 1992), pp. 1–23.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986).

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Figures (15)

Fig. 1
Fig. 1

Block diagram of the c/d/c processing mode.

Fig. 2
Fig. 2

Simulation of (a) a continuous target L(x, y) and (b) its corresponding discrete image s(x, y) displayed on a 256 × 256 pixel processing lattice with X = Y = 1/4.

Fig. 3
Fig. 3

Image components: (a) The continuous optical image and its components, the target power spectral density (PSD) and the optical response. (b) The sampled discrete image and its components, blurring and aliasing.

Fig. 4
Fig. 4

(a) R d (x, y), the display of the acquired signal without c/d/c digital processing. (b) R r (x, y), the display of the same acquired signal after c/d/c digital processing.

Fig. 5
Fig. 5

Optimal optical designs obtained by use of (a) information and (b) fidelity as functions of the available SNR.

Fig. 6
Fig. 6

Images acquired with different camera optical designs and a fixed value of Kσ L n = 32 and their corresponding performance metrics: (a) ρ c = 0.45, ℋ = 2.76, and ℱ = 0.714. (b) More blurring: ρ c = 0.3, ℋ = 2.12, and ℱ = 0.679. (c) More aliasing: ρ c = 0.8, ℋ = 1.97, and ℱ = 0.704.

Fig. 7
Fig. 7

Optimal quantization design obtained by use of (a) the information and (b) the fidelity metrics. The final requantization for each design is marked on the figure.

Fig. 8
Fig. 8

Example images for c/d/c OE acquisition, a transmission design optimized by information (Table 1), and a fixed display design of ρ d = 0.37 and ι = 128 with no digital processing: (a) The original target. (b) Kσ L n = 16, ρ c = 0.51, η = 5, and ℱ d = 0.435. (c) Kσ L n = 32, ρ c = 0.45, η = 6, and ℱ d = 0.420. (d) Kσ L n = 64, ρ c = 0.39, η = 7, and ℱ d = 0.400. (e) Kσ L n = 128, ρ c = 0.36, η = 8, and ℱ d = 0.387. (f) Kσ L n = 256, ρ c = 0.33, η = 9, and ℱ d = 0.372.

Fig. 9
Fig. 9

Example images for c/d/c OED acquisition, a transmission design optimized by use of the information metric, and a fixed display design of ρ d = 0.37 and ι = 128: (a) The original target. (b) Kσ L n = 16, ρ c = 0.51, η = 5, ℋ d = 1.82, and ℱ r = 0.695. (c) Kσ L n = 32, ρ c = 0.45, η = 6, ℋ d = 2.23, and ℱ r = 0.705. (d) Kσ L n = 64, ρ c = 0.39, η = 7, ℋ d = 2.45, and ℱ r = 0.706. (e) Kσ L n = 128, ρ c = 0.36, η = 8, ℋ d = 2.53, and ℱ r = 0.705. (f) Kσ L n = 256, ρ c = 0.33, η = 9, ℋ d = 2.47, and ℱ r = 0.701.

Fig. 10
Fig. 10

Example images for c/d/c OED acquisition, a transmission design optimized by use of the fidelity metric, and a fixed display design of ρ d = 0.37 and ι = 128: (a) The original target. (b) Kσ L n = 16, ρ c = 0.57, η = 6, ℋ d = 1.96, and ℱ r = 0.702. (c) Kσ L n = 32, ρ c = 0.49, η = 6, ℋ d = 2.25, and ℱ r = 0.707. (d) Kσ L n = 64, ρ c = 0.43, η = 7, ℋ d = 2.51, and ℱ r = 0.710. (e) Kσ L n = 128, ρ c = 0.39, η = 7, ℋ d = 2.54, and ℱ r = 0.708. (f) Kσ L n = 256, ρ c = 0.35, η = 8, ℋ d = 2.49, and ℱ r = 0.704.

Fig. 11
Fig. 11

Optimal display for information and fidelity. Display SNR σ L d : 4 (·····), 6 (----), 8 (-·-·-), 10 (——), 16 (—···—), 64 (——).

Fig. 12
Fig. 12

System performance for the parameters specified in Tables 1 and 2: (a) The throughput response of the OE imaging system. (b) The c/d/c digital filter response. (c) The throughput response of the OED imaging system.

Fig. 13
Fig. 13

Examples images for informationally optimized OED design and processing: (a) The original target. (b) Kσ L n = 16, ρ c = 0.51, η = 5, ρ d = 1.02, ι = 64 or σ R d = 8, ℋ d = 1.90, and ℱ d = 0.697. (c) Kσ L n = 32, ρ c = 0.44, η = 6, ρ d = 0.66, ι = 100 or σ R d = 10, ℋ d = 2.42, and ℱ d = 0.711. (d) Kσ L n = 64, ρ c = 0.39, η = 7, ρ d = 0.55, ι = 256 or σ K d = 16, ℋ d = 3.01, and ℱ d = 0.715. (e) Kσ L n = 128, ρ c = 0.36, η = 8, ρ d = 0.39, ι = 1024 or σ K d = 32, ℋ d = 3.60, and ℱ d = 0.718. (f) Kσ L n = 256, ρ c = 0.33, η = 9, ρ d = 0.35, ι = 4096 or σ R d = 64, ℋ d = 4.12, and ℱ d = 0.719.

Fig. 14
Fig. 14

Example images for fidelity-optimized OED optimal design and processing: (a) The original target. (b) Kσ L n = 16, ρ c = 0.57, η = 6, ρ d = 0.90, ι = 64 or σ R d = 8, ℋ d = 2.04, and ℱ d = 0.704. (c) Kσ L n = 32, ρ c = 0.49, η = 6, ρ d = 0.94, ι = 100 or σ R d = 10, ℋ d = 2.45, and ℱ d = 0.711. (d) Kσ L n = 64, ρ c = 0.43, η = 7, ρ d = 1.02, ι = 256 or σ R d = 16, ℋ d = 3.05, and ℱ d = 0.717. (e) Kσ L n = 128, ρ c = 0.39, η = 7, ρ d = 1.06, ι = 512 or σ R d = 23, ℋ d = 3.35, and ℱ d = 0.718. (f) Kσ L n = 256, ρ c = 0.35, η = 8, ρ d = 1.10, ι = 625 or σ R d = 25, ℋ d = 3.91, and ℱ d = 0.720.

Fig. 15
Fig. 15

Example images of c/d/c optimal-constraint OED designs: (a) Unconstrained: Kσ L n = 256, ρ c = 0.36, η = 8, ρ d = 1.06, ι = 256, and ℋ d = 3.70. (b) Fixed display: Kσ L n = 256, ρ c = 0.47, η = 8, ρ d = 0.45, ι = 64, and ℋ d = 2.37. (c) Constrained transmission: Kσ L n = 256, ρ c = 0.48, η = 6, ρ d = 0.45, ι = 64, and ℋ d = 2.25. (d) Improved display: Kσ L n = 256, ρ c = 0.43, η = 6, ρ d = 0.90, ι = 128, and ℋ d = 2.79.

Tables (2)

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Table 1 Optimized Imaging Designs Constrained by the Available SNR KσLn

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Table 2 Optimized Displays for Optimized Acquisition and Transmission

Equations (35)

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fx, y=XY m,n fmX, nYδx-mX, y-nY.
f˜υ, ω=m,n fmX, nYexp-2πimXυ+nYω.
|||¯|||¯x, y=XY n,m δx-mX, y-nY,
|||ˆ¯|||ˆ¯υ, ω=n,m δυ-m/X, ω-n/Y=δυ, ω+|||ˆ¯sυ, ω,
Bˆ=1for |υ|<1/2X0elsewhere, |ω|<1/2Y.
sx, y=KLx, y * τx, y|||¯+nx, y,
s˜υ, ω=KLˆυ, ωτˆυ, ω * |||ˆ¯+ñυ, ω.
Φ˜qυ, ω=σq2=σs2/κ2.
RD=max0, 12, 12log2σs2D=max0, 1/2, η.
Φ˜sυ, ω=ΦˆLυ, ω|τˆυ, ω|2 * |||ˆ¯+Φ˜nυ, ω=ΦˆLυ, ω|τˆυ, ω|2+ΦˆLυ, ω|τˆυ, ω|2 * |||ˆ¯s+Φ˜nυ, ω=Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω,
Φ˜seυ, ω=Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω.
σs2= Bˆ Φ˜sυ, ωdυdω= BˆΦˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ωdυdω,
σse2= Bˆ Φ˜seυ, ωdυdω
= BˆΦˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ωdυdω.
Rdx, y=sex, y * τdx, y+ndx, y,
Φˆddυ, ω=Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|τˆdυ, ω|2.
Ψˆυ, ω=ΦˆLυ, ωτˆ*υ, ωτˆd*υ, ωΦˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|τˆdυ, ω|2+Φ˜dυ, ω.
sˆdυ, ω=K-1s˜eυ, ωΨˆυ, ω.
Ψˆυ, ω; f=ΦˆLυ, ωτˆ*υ, ωf˜*υ, ωτˆd*υ, ωΦˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|f˜υ, ω|2|τˆdυ, ω|2+Φ˜dυ, ω,
Rrx, y=sdx, y * τdx, y+ndx, y=sex, y * Ψx, y * τdx, y+ndx, y,
Φˆdrυ, ω=ΦˆLυ, ω|τˆυ, ω|2|τˆdυ, ω|2.
Γˆdυ, ω=τˆυ, ωτˆdυ, ω,
Γˆrυ, ω=τˆυ, ωΨˆυ, ωτˆdυ, ω=Φˆbυ, ω|τˆdυ, ω|2Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|τˆdυ, ω|2+Φ˜dυ, ω.
d2=-ΦˆLυ, ω1-Γˆdυ, ω+Φ˜dυ, ωdυdω.
d2=σL2-- ΦˆLυ, ωΓˆdυ, ωdυdω+σdd2.
r2=-ΦˆLυ, ω1-Γˆrυ, ω+Φ˜dυ, ωdυdω.
r2=σL2-- ΦˆLυ, ωΓˆrυ, ωdυdω+σdr2.
d=1-d2σL2.
d=σL-2 - ΦˆLυ, ωΓˆdυ, ωdυdω-σdd/σL2.
r=1-r2σL2.
r=σL-2 - ΦˆLυ, ωΓˆrυ, ωdυdω-σdr/σL2.
=12 Bˆlog2 Φ˜sυ, ωdυdω-12 Bˆlog2Φˆaυ, ω+Φ˜nυ, ωdυdω=12 Bˆlog2Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ωΦˆaυ, ω+Φ˜nυ, ωdυdω=12 Bˆlog21+Φˆbυ, ωΦˆaυ, ω+Φ˜nυ, ωdυdω=-12 Bˆlog21-Φˆbυ, ωΦˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ωdυdω,
e=12 Bˆlog21+Φˆbυ, ωΦˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ωdυdω.
d=12 Bˆlog21+Φˆbυ, ω|τˆdυ, ω|2Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|τˆdυ, ω|2+Φ˜dυ, ωdυdω=-12 Bˆlog21-Φˆbυ, ω|τˆdυ, ω|2Φˆbυ, ω+Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|τˆdυ, ω|2+Φ˜dυ, ωdυdω=-12 Bˆlog21-τˆυ, ωΨˆυ, ωτˆdυ, ωdυdω=-12 Bˆlog21-Γˆrυ, ωdυdω.
f=12 Bˆlog21+Φˆbυ, ω|f˜υ, ω|2|τˆdυ, ω|2Φˆaυ, ω+Φ˜nυ, ω+Φ˜qυ, ω|f˜υ, ω|2|τˆdυ, ω|2+Φ˜dυ, ωdυdω.

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