Abstract

Pixel signal-to-noise ratio is one accepted measure of image quality for predicting observer performance in medical imaging. We have found, however, that images with equal pixel signal-to-noise ratio (SNRp) but different correlation properties give quite different observer-performance measures for a simple detection experiment. The SNR at the output of an ideal detector with the ability to prewhiten the noise is also a poor predictor of human performance for disk signals in high-pass noise. We have found constant observer efficiencies for humans relative to the performance of a nonprewhitening detector for this task.

© 1985 Optical Society of America

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References

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  1. R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
    [CrossRef]
  2. A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of IEEE Computer Society International Workshop on Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982).
  3. A. E. Burgess, R. F. Wagner, R. J. Jennings, “On SNR requirements for medical images,” in Proceedings of IEEE Computer Society International Symposium on Medical Imaging and Image Interpretation (Institute of Electrical and Electronics Engineers, New York, 1982).
  4. S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the IVth International Conference on Information Processing in Scintigraphy (Commissariat à l′Energie Atomique, Orsay, France, 1975).
  5. P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
    [CrossRef] [PubMed]
  6. P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163–1176 (1982).
    [CrossRef] [PubMed]
  7. K. M. Hanson, “Detectability in the presence of computed tomographic reconstruction noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 127, 304–312 (1977).
  8. H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.
  9. B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
    [CrossRef] [PubMed]
  10. G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
    [CrossRef]
  11. D. B. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  12. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. I–III.
  13. C. E. Metz, “Empirical evidence of imaging procedures in terms of information content and receiver operating characteristic curves,” J. Nucl. Med. 13, 453 (1972).
  14. T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
    [CrossRef] [PubMed]
  15. C. E. Metz, “Basic principles of ROC analysis,” Sem. Nucl. Med. 8, 283–298 (1978).
    [CrossRef]
  16. D. A. Turner, “An intuitive approach to receiver operating characteristic curve analysis,” J. Nucl. Med. 19, 213–220 (1978).
    [PubMed]
  17. J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 14, 109–121 (1979).
    [CrossRef] [PubMed]
  18. J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
  19. W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
    [CrossRef]
  20. D. D. Dorfman, E. Alf, “Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals-rating method data,” J. Math. Psych. 6, 487–496 (1969).
    [CrossRef]
  21. J. A. Hanley, B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143, 29–36 (1982).
    [PubMed]
  22. C. E. Cook, M. Bernfeld, Radar Signals: An Introduction to Theory and Applications (Academic, New York, 1967).
  23. A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).
  24. H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1978).
    [CrossRef]
  25. A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
    [CrossRef] [PubMed]
  26. R. F. Wagner, D. G. Brown, “More unified analysis of medical imaging system SNR characteristics,” Proc. Soc. Photo-Opt. Instrum. Eng. 454, 2–8 (1984).
  27. Although the efficiency value for n= 4 seems high in comparison with the other three efficiency values, this number is not significantly different from the others. This is simply due to the fact that this ηnpwis the ratio of two very small numbers, the first and third elements of the column for n= 4. We should expect a large error in this value from Fig. 14.

1984 (1)

R. F. Wagner, D. G. Brown, “More unified analysis of medical imaging system SNR characteristics,” Proc. Soc. Photo-Opt. Instrum. Eng. 454, 2–8 (1984).

1982 (4)

J. A. Hanley, B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143, 29–36 (1982).
[PubMed]

A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163–1176 (1982).
[CrossRef] [PubMed]

G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
[CrossRef]

1981 (2)

P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
[CrossRef] [PubMed]

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

1979 (1)

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 14, 109–121 (1979).
[CrossRef] [PubMed]

1978 (3)

H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

C. E. Metz, “Basic principles of ROC analysis,” Sem. Nucl. Med. 8, 283–298 (1978).
[CrossRef]

D. A. Turner, “An intuitive approach to receiver operating characteristic curve analysis,” J. Nucl. Med. 19, 213–220 (1978).
[PubMed]

1977 (1)

K. M. Hanson, “Detectability in the presence of computed tomographic reconstruction noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 127, 304–312 (1977).

1975 (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

1974 (1)

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

1973 (1)

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

1972 (1)

C. E. Metz, “Empirical evidence of imaging procedures in terms of information content and receiver operating characteristic curves,” J. Nucl. Med. 13, 453 (1972).

1969 (1)

D. D. Dorfman, E. Alf, “Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals-rating method data,” J. Math. Psych. 6, 487–496 (1969).
[CrossRef]

1958 (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Alf, E.

D. D. Dorfman, E. Alf, “Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals-rating method data,” J. Math. Psych. 6, 487–496 (1969).
[CrossRef]

Anderson, T. M.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Barlow, H. B.

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

Bernfeld, M.

C. E. Cook, M. Bernfeld, Radar Signals: An Introduction to Theory and Applications (Academic, New York, 1967).

Birdsall, T. G.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Borgstrom, M. C.

G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
[CrossRef]

Bostrom, R. G.

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

Brown, D. G.

R. F. Wagner, D. G. Brown, “More unified analysis of medical imaging system SNR characteristics,” Proc. Soc. Photo-Opt. Instrum. Eng. 454, 2–8 (1984).

Burgess, A. E.

A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of IEEE Computer Society International Workshop on Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, “On SNR requirements for medical images,” in Proceedings of IEEE Computer Society International Symposium on Medical Imaging and Image Interpretation (Institute of Electrical and Electronics Engineers, New York, 1982).

Cook, C. E.

C. E. Cook, M. Bernfeld, Radar Signals: An Introduction to Theory and Applications (Academic, New York, 1967).

Denny, E. W.

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

Dorfman, D. D.

D. D. Dorfman, E. Alf, “Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals-rating method data,” J. Math. Psych. 6, 487–496 (1969).
[CrossRef]

Green, D. B.

D. B. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Guignard, P. A.

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163–1176 (1982).
[CrossRef] [PubMed]

Hanley, J. A.

J. A. Hanley, B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143, 29–36 (1982).
[PubMed]

Hanson, K. M.

K. M. Hanson, “Detectability in the presence of computed tomographic reconstruction noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 127, 304–312 (1977).

Hoffer, P. B.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Jennings, R. J.

A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

A. E. Burgess, R. F. Wagner, R. J. Jennings, “On SNR requirements for medical images,” in Proceedings of IEEE Computer Society International Symposium on Medical Imaging and Image Interpretation (Institute of Electrical and Electronics Engineers, New York, 1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of IEEE Computer Society International Workshop on Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982).

Judy, P. F.

P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
[CrossRef] [PubMed]

Julesz, B.

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Lusted, L. B.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Mazzeo, J.

G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
[CrossRef]

McNeil, B. J.

J. A. Hanley, B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143, 29–36 (1982).
[PubMed]

Metz, C. E.

C. E. Metz, “Basic principles of ROC analysis,” Sem. Nucl. Med. 8, 283–298 (1978).
[CrossRef]

C. E. Metz, “Empirical evidence of imaging procedures in terms of information content and receiver operating characteristic curves,” J. Nucl. Med. 13, 453 (1972).

Mintzer, R. A.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Pickett, R. M.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).

Pizer, S. M.

S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the IVth International Conference on Information Processing in Scintigraphy (Commissariat à l′Energie Atomique, Orsay, France, 1975).

Pokorny, J.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Seeley, G. W.

G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
[CrossRef]

Smith, V. C.

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

Swensson, R. G.

P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
[CrossRef] [PubMed]

Swets, J. A.

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 14, 109–121 (1979).
[CrossRef] [PubMed]

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).

D. B. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

Tanner, W. P.

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

Todd-Pokropek, A. E.

S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the IVth International Conference on Information Processing in Scintigraphy (Commissariat à l′Energie Atomique, Orsay, France, 1975).

Turner, D. A.

D. A. Turner, “An intuitive approach to receiver operating characteristic curve analysis,” J. Nucl. Med. 19, 213–220 (1978).
[PubMed]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. I–III.

Wagner, R. F.

R. F. Wagner, D. G. Brown, “More unified analysis of medical imaging system SNR characteristics,” Proc. Soc. Photo-Opt. Instrum. Eng. 454, 2–8 (1984).

A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of IEEE Computer Society International Workshop on Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, “On SNR requirements for medical images,” in Proceedings of IEEE Computer Society International Symposium on Medical Imaging and Image Interpretation (Institute of Electrical and Electronics Engineers, New York, 1982).

Weaver, K. E.

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

Behavior Res. Methods Instrum. (1)

G. W. Seeley, M. C. Borgstrom, J. Mazzeo, “A general interactive computer program for running signal detection experiments,” Behavior Res. Methods Instrum. 4, 555–556 (1982).
[CrossRef]

Invest. Radiol. (2)

T. M. Anderson, R. A. Mintzer, P. B. Hoffer, L. B. Lusted, V. C. Smith, J. Pokorny, “Nuclear image transmission by Picturephone: evaluation by ROC curve method,” Invest. Radiol. 8, 244–250 (1973).
[CrossRef] [PubMed]

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 14, 109–121 (1979).
[CrossRef] [PubMed]

J. Acoust. Soc. Am. (1)

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958).
[CrossRef]

J. Appl. Photo. Eng. (1)

A. E. Burgess, R. J. Jennings, R. F. Wagner, “Statistical efficiency: a measure of human visual signal-detection performance,” J. Appl. Photo. Eng. 8, 76–78 (1982).

J. Math. Psych. (1)

D. D. Dorfman, E. Alf, “Maximum likelihood estimation of parameters of signal detection theory and determination of confidence intervals-rating method data,” J. Math. Psych. 6, 487–496 (1969).
[CrossRef]

J. Nucl. Med. (2)

D. A. Turner, “An intuitive approach to receiver operating characteristic curve analysis,” J. Nucl. Med. 19, 213–220 (1978).
[PubMed]

C. E. Metz, “Empirical evidence of imaging procedures in terms of information content and receiver operating characteristic curves,” J. Nucl. Med. 13, 453 (1972).

Med. Phys. (2)

R. F. Wagner, K. E. Weaver, E. W. Denny, R. G. Bostrom, “Toward a unified view of radiological imaging systems, Part 1: noiseless images,” Med. Phys. 1, 11–24 (1974).
[CrossRef]

P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
[CrossRef] [PubMed]

Phys. Med. Biol. (1)

P. A. Guignard, “A comparative method based on ROC analysis for the quantitation of observer performance in scintigraphy,” Phys. Med. Biol. 27, 1163–1176 (1982).
[CrossRef] [PubMed]

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

K. M. Hanson, “Detectability in the presence of computed tomographic reconstruction noise,” Proc. Soc. Photo-Opt. Instrum. Eng. 127, 304–312 (1977).

R. F. Wagner, D. G. Brown, “More unified analysis of medical imaging system SNR characteristics,” Proc. Soc. Photo-Opt. Instrum. Eng. 454, 2–8 (1984).

Radiology (1)

J. A. Hanley, B. J. McNeil, “The meaning and use of the area under a receiver operating characteristic (ROC) curve,” Radiology 143, 29–36 (1982).
[PubMed]

Sci. Am. (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Science (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual signal discrimination,” Science 214, 93–94 (1981).
[CrossRef] [PubMed]

Sem. Nucl. Med. (1)

C. E. Metz, “Basic principles of ROC analysis,” Sem. Nucl. Med. 8, 283–298 (1978).
[CrossRef]

Vision Res. (1)

H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1978).
[CrossRef]

Other (9)

C. E. Cook, M. Bernfeld, Radar Signals: An Introduction to Theory and Applications (Academic, New York, 1967).

Although the efficiency value for n= 4 seems high in comparison with the other three efficiency values, this number is not significantly different from the others. This is simply due to the fact that this ηnpwis the ratio of two very small numbers, the first and third elements of the column for n= 4. We should expect a large error in this value from Fig. 14.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).

D. B. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. I–III.

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, New York, 1981), Vols. I and II.

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of IEEE Computer Society International Workshop on Medical Imaging (Institute of Electrical and Electronics Engineers, New York, 1982).

A. E. Burgess, R. F. Wagner, R. J. Jennings, “On SNR requirements for medical images,” in Proceedings of IEEE Computer Society International Symposium on Medical Imaging and Image Interpretation (Institute of Electrical and Electronics Engineers, New York, 1982).

S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the IVth International Conference on Information Processing in Scintigraphy (Commissariat à l′Energie Atomique, Orsay, France, 1975).

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Figures (14)

Fig. 1
Fig. 1

a, Point-source object; b, image of point source is ensemble of points with centroid at actual source location; c, blurred image resulting from postprocessing filters is sum of individually blurred point images.

Fig. 2
Fig. 2

Generalized model of nuclear-medicine imaging system. Object is convolved first with psf p1(r). Poisson noise is then added, followed by filtering with p2(r) to form the final image.

Fig. 3
Fig. 3

Power spectrum of an image formed by imaging system with low-pass postprocessing filter. In this and all following figures, a pixel in Fourier space measures 0.0125 cycles per millimeter along each side.

Fig. 4
Fig. 4

Power spectrum of an image formed by the imaging system with a high-pass postprocessing filter.

Fig. 5
Fig. 5

Profile of disk object showing ramp edge.

Fig. 6
Fig. 6

Set of hypothetical ROC curves indicating general shape of curve for different imaging-system performance. Curve I gives the worst performance of the set (d′ = 0.5). Curve IV gives the best performance of the set (d′ = 2.0).

Fig. 7
Fig. 7

ROC curves generated by human-observer-performance data for the high-pass and low-pass images. The low-pass images give much better detection ability than the high-pass images.

Fig. 8
Fig. 8

Block diagram showing processing steps performed by an ideal observer with the ability to prewhiten the image noise.

Fig. 9
Fig. 9

Postprocessing filters used to test ideal-observer SNR prediction capability. For each value of n, the filters peak at the same pixel value (ρ = 8.6 pixels).

Fig. 10
Fig. 10

Power spectrum for images generated by transfer functions shown in Fig. 9. The value of n determines the slope of the function at low spatial frequency.

Fig. 11
Fig. 11

ROC curves generated by human-performance data for images with equal SNRideal as a function of n. As n increases human performance degrades, as is evidenced by the decrease in the area under the curve.

Fig. 12
Fig. 12

Block diagram illustrating the processing steps performed by an ideal observer without the ability to prewhiten the image noise.

Fig. 13
Fig. 13

Area under the ROC curve for each value of the filter parameter n, with corresponding error bars.

Fig. 14
Fig. 14

Detectability d′ derived from the areas under the ROC curves of Fig. 13.

Tables (3)

Tables Icon

Table 1 Certainty Scale

Tables Icon

Table 2 Efficiency for Images Containing Correlated Noise as a Function of the Filter Parameter n

Tables Icon

Table 3 Efficiency for Images Containing White Noise

Equations (30)

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

p 1 ( r ) * * p 2 ( r ) = p T ( r )
P 1 ( ρ ) P 2 ( ρ ) = P T ( ρ ) .
P T ( ρ ) = exp ( β T 2 ρ 2 ) ,
P 2 ( ρ ) = exp ( β 2 2 ρ 2 ) .
P 1 ( ρ ) = exp ( β 1 2 ρ 2 ) ,
β 1 2 + β 2 2 = β T 2 .
β 1 = 3 β 2 .
P 2 ( ρ ) = ( 1 + α 2 ρ 2 ) exp ( β T 2 ρ 2 ) ,
P 1 ( ρ ) = ( 1 + α 2 ρ 2 ) 1 .
TPF = number of images called signal correctly total number of images containing signal .
FPF = number of images called signal incorrectly total number of images containing signal .
P 2 ( ρ ) = | ρ Δ ρ | n / 2 exp ( β 2 2 ρ 2 )
P 1 ( ρ ) = | ρ Δ ρ | n / 2 exp ( β 1 2 ρ 2 )
β 1 2 + β 2 2 = β T 2 .
η = [ d SNR ideal ] 2 .
η = [ d SNR ideal ] 2 [ SNR ideal npw SNR ideal npw ] 2 = [ d SNR ideal npw ] 2 [ SNR ideal npw SNR ideal ] 2 = [ η npw ] × [ observer reconstruction penalty ] .
SNR ideal npw
S 0 = A S ( ξ , η ) P 1 ( ξ , η ) P 2 ( ξ , η ) d ξ d η ,
N ( ξ , η ) = N 0 | P 2 ( ξ , η ) | 2 ,
σ 0 2 = N ( ξ , η ) d ξ d η .
SNR p = S 0 σ 0 = A S ( ξ , η ) P 1 ( ξ , η ) P 2 ( ξ , η ) d ξ d η [ N 0 | P 2 ( ξ , η ) | 2 d ξ d η ] 1 / 2 .
S = A S ( ξ , η ) P 1 ( ξ , η ) P 2 ( ξ , η ) O ( ξ , η ) d ξ d η .
σ 2 = N ( ξ , η ) | O ( ξ , η ) | 2 d ξ d η = N 0 | P 2 ( ξ , η ) | 2 | O ( ξ , η ) | 2 d ξ d η .
S σ = A S ( ξ , η ) P 1 ( ξ , η ) P 2 ( ξ , η ) O ( ξ , η ) d ξ d η [ N 0 | P 2 ( ξ , η ) | 2 | O ( ξ , η ) | 2 d ξ d η ] 1 / 2 .
O ( ξ , η ) = S * ( ξ , η ) P 1 * ( ξ , η ) P 2 ( ξ , η ) .
SNR ideal npw = A | S ( ξ , η ) | 2 | P 1 ( ξ , η ) | 2 | P 2 ( ξ , η ) | 2 d ξ d η [ N 0 | S ( ξ , η ) 2 | P 1 ( ξ , η ) | 2 | P 2 ( ξ , η ) | 4 d ξ d η ] 1 / 2 .
S = A S ( ξ , η ) P 1 ( ξ , η ) P 2 ( ξ , η ) N 1 / 2 ( ξ , η ) O ( ξ , η ) d ξ d η .
σ 2 = N 0 | P 2 ( ξ , η ) | 2 [ N ( ξ , η ) 1 / 2 ] 2 | O ( ξ , η ) | 2 d ξ d η = | O ( ξ , η ) | 2 d ξ d η .
O ( ξ , η ) = S * ( ξ , η ) P 1 * ( ξ , η ) P 2 * ( ξ , η ) [ N ( ξ , η ) ] 1 / 2 ,
SNR ideal pw = A | S ( ξ , η ) | 2 | P 1 ( ξ , η ) | 2 | P 2 ( ξ , η ) | 2 N 1 ( ξ , η ) d ξ d η [ | S ( ξ , η ) | 2 | P 1 ( ξ , η ) | 2 | P 2 ( ξ , η ) | 2 N 1 ( ξ , η ) d ξ d η ] 1 / 2 , SNR ideal pw = A [ | S ( ξ , η ) | 2 | P 1 ( ξ , η ) | 2 | P 2 ( ξ , η ) | 2 N 1 ( ξ , η ) d ξ d η ] 1 / 2 SNR ideal pw = A [ | S ( ξ , η ) | 2 | P 1 ( ξ , η ) | 2 d ξ d η N 0 ] 1 / 2 . .

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