Abstract

Several authors have measured the detection ability of human observers for objects in correlated (nonwhite) noise. These studies have shown that the human observer has approximately constant efficiency when compared with a nonprewhitening ideal observer. In this paper we add a frequency-selective mechanism to the ideal-observer model, similar to the channel mechanism that has been demonstrated through experiments that measure a subject’s ability to detect grating stimuli. For a number of detection and discrimination tasks, the nonprewhitening ideal-observer model and the channelized ideal-observer model yield similar performance predictions. Thus both models seem equally capable of explaining a considerable body of psychophysical data, and it would be difficult to devise an experiment to determine which model is more nearly correct.

© 1987 Optical Society of America

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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 the International Workshop on Physics and Engineering in Medical Images, O. Nalcioglu, J. M. S. Prewitt, eds. (Institute of Electrical and Electronics Engineers, New York, 1982).
    [Crossref]
  3. A. E. Burgess, “Statistical efficiency of perceptual decisions,” in Application of Optical Instrumentation in Medicine XII: Medical Image Production, Processing, Display, and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.454, 18–26 (1984).
    [Crossref]
  4. R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
    [Crossref]
  5. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, G. W. Seeley, “Effect of noise correlation on detectability of disk signals in medical imaging,” J. Opt. Soc. Am. A 2, 1752–1759 (1985).
    [Crossref] [PubMed]
  6. H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1978).
    [Crossref]
  7. S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 15–19.
  8. P. F. Judy, R. G. Swensson, “Lesion detection and signal-to-noise ratio in CT images,” Med. Phys. 8, 13–23 (1981).
    [Crossref] [PubMed]
  9. 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]
  10. O. H. Schade, “Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems,”RCA Rev. 9, 5–37 (1948).
  11. K. J. Rosenbruch, “The contrast sensitivity of the eye as a factor in the evaluation of optical images,” Optik 16, 135–45 (1959).
  12. J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system,”J. Opt. Soc. Am. 228, 328–335 (1962).
    [Crossref]
  13. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).
  14. M. Sachs, J. Nachmias, J. Robson, “Spatial-frequency channels in human vision,”J. Opt. Soc. Am. 61, 1176–1186 (1971).
    [Crossref] [PubMed]
  15. N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single channel and multichannels models,” Vision Res. 11, 251–259 (1971).
    [Crossref] [PubMed]
  16. H. Mostafavi, D. Sakrison, “Structure and properties of a single channel in the human visual system,” Vision Res. 16, 957–968 (1976).
    [Crossref] [PubMed]
  17. C. F. Strohmeyer, B. Julesz, “Spatial-frequency masking in vision: critical bands and spread of masking,”J. Opt. Soc. Am. 62, 1221–1232 (1972).
    [Crossref]
  18. M. Halter, “On the spatial breadth of spatial frequency channels in human visual detection,” doctoral dissertation (University of California, Berkeley, Calif., 1976).
  19. G. B. Henning, B. G. Hertz, J. L. Hinton, “Effects of different hypothetical detection mechanisms on the shape of spatial-frequency filters inferred from masking experiments. I. Noise masks,”J. Opt. Soc. Am. 71, 574–81 (1981).
    [Crossref] [PubMed]
  20. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.
  21. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966).
  22. J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
  23. D. J. Goodenough, C. E. Metz, “Implications of a noisy observer to data processing techniques,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 400–419.
  24. D. G. Pelli, “Effects of visual noise,” doctoral dissertation (Cambridge University, Cambridge, 1980).
  25. R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 9, 521–534 (1981).
    [Crossref]
  26. M. S. Chesters, G. A. Hay, “Quantitative relation between detectability and noise power,” Phys. Med. Biol. 28, 1113–1125 (1983).
    [Crossref]
  27. H.-P. Chan, C. E. Metz, K. Doi, “Digital image processing: optimal spatial filter for maximization of the perceived SNR based on a statistical decision theory model for the human observer,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 2–11 (1985).
    [Crossref]
  28. A. E. Burgess, “On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV and Picture Archiving and Communication Systems, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 208–213 (1986).
    [Crossref]
  29. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).
  30. D. Gabor, “Theory of communication,” J. IEE (London) 93, 429–457 (1946).
  31. S. Marcelja, “Mathematical description of the responses of simple cortical cells,”J. Opt. Soc. Am. 70, 1297–1300 (1980).
    [Crossref] [PubMed]
  32. J. D. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1982).
    [Crossref]
  33. A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983).
    [Crossref]
  34. K. J. Myers, “Visual perception in correlated noise,” doctoral dissertation (University of Arizona, Tucson, Ariz., 1985).
  35. G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
    [Crossref]
  36. J. Nachmias, B. E. Rogowitz, “Masking by spatially modulated gratings,” Vision Res. 23, 1621–1629 (1983).
    [Crossref]

1985 (2)

1983 (2)

M. S. Chesters, G. A. Hay, “Quantitative relation between detectability and noise power,” Phys. Med. Biol. 28, 1113–1125 (1983).
[Crossref]

J. Nachmias, B. E. Rogowitz, “Masking by spatially modulated gratings,” Vision Res. 23, 1621–1629 (1983).
[Crossref]

1982 (2)

J. D. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1982).
[Crossref]

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]

1981 (3)

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

G. B. Henning, B. G. Hertz, J. L. Hinton, “Effects of different hypothetical detection mechanisms on the shape of spatial-frequency filters inferred from masking experiments. I. Noise masks,”J. Opt. Soc. Am. 71, 574–81 (1981).
[Crossref] [PubMed]

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 9, 521–534 (1981).
[Crossref]

1980 (1)

1978 (1)

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

1976 (1)

H. Mostafavi, D. Sakrison, “Structure and properties of a single channel in the human visual system,” Vision Res. 16, 957–968 (1976).
[Crossref] [PubMed]

1975 (1)

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[Crossref]

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]

1972 (1)

1971 (2)

M. Sachs, J. Nachmias, J. Robson, “Spatial-frequency channels in human vision,”J. Opt. Soc. Am. 61, 1176–1186 (1971).
[Crossref] [PubMed]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single channel and multichannels models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

1968 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

1962 (1)

J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system,”J. Opt. Soc. Am. 228, 328–335 (1962).
[Crossref]

1959 (1)

K. J. Rosenbruch, “The contrast sensitivity of the eye as a factor in the evaluation of optical images,” Optik 16, 135–45 (1959).

1948 (1)

O. H. Schade, “Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems,”RCA Rev. 9, 5–37 (1948).

1946 (1)

D. Gabor, “Theory of communication,” J. IEE (London) 93, 429–457 (1946).

Barlow, H. B.

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

Barrett, H. H.

Borgstrom, M. C.

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]

Broadbent, D. E.

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[Crossref]

Brown, D. G.

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[Crossref]

Burgess, A. E.

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the International Workshop on Physics and Engineering in Medical Images, O. Nalcioglu, J. M. S. Prewitt, eds. (Institute of Electrical and Electronics Engineers, New York, 1982).
[Crossref]

A. E. Burgess, “Statistical efficiency of perceptual decisions,” in Application of Optical Instrumentation in Medicine XII: Medical Image Production, Processing, Display, and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.454, 18–26 (1984).
[Crossref]

A. E. Burgess, “On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV and Picture Archiving and Communication Systems, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 208–213 (1986).
[Crossref]

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Chan, H.-P.

H.-P. Chan, C. E. Metz, K. Doi, “Digital image processing: optimal spatial filter for maximization of the perceived SNR based on a statistical decision theory model for the human observer,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 2–11 (1985).
[Crossref]

Chesters, M. S.

M. S. Chesters, G. A. Hay, “Quantitative relation between detectability and noise power,” Phys. Med. Biol. 28, 1113–1125 (1983).
[Crossref]

Daugman, J. D.

J. D. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1982).
[Crossref]

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]

DePalma, J. J.

J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system,”J. Opt. Soc. Am. 228, 328–335 (1962).
[Crossref]

Doi, K.

H.-P. Chan, C. E. Metz, K. Doi, “Digital image processing: optimal spatial filter for maximization of the perceived SNR based on a statistical decision theory model for the human observer,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 2–11 (1985).
[Crossref]

Gabor, D.

D. Gabor, “Theory of communication,” J. IEE (London) 93, 429–457 (1946).

Goodenough, D. J.

D. J. Goodenough, C. E. Metz, “Implications of a noisy observer to data processing techniques,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 400–419.

Graham, N.

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single channel and multichannels models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

Green, D. M.

D. M. 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]

Halter, M.

M. Halter, “On the spatial breadth of spatial frequency channels in human visual detection,” doctoral dissertation (University of California, Berkeley, Calif., 1976).

Hay, G. A.

M. S. Chesters, G. A. Hay, “Quantitative relation between detectability and noise power,” Phys. Med. Biol. 28, 1113–1125 (1983).
[Crossref]

Henning, G. B.

G. B. Henning, B. G. Hertz, J. L. Hinton, “Effects of different hypothetical detection mechanisms on the shape of spatial-frequency filters inferred from masking experiments. I. Noise masks,”J. Opt. Soc. Am. 71, 574–81 (1981).
[Crossref] [PubMed]

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[Crossref]

Hertz, B. G.

G. B. Henning, B. G. Hertz, J. L. Hinton, “Effects of different hypothetical detection mechanisms on the shape of spatial-frequency filters inferred from masking experiments. I. Noise masks,”J. Opt. Soc. Am. 71, 574–81 (1981).
[Crossref] [PubMed]

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[Crossref]

Hinton, J. L.

Jennings, R. J.

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the International Workshop on Physics and Engineering in Medical Images, O. Nalcioglu, J. M. S. Prewitt, eds. (Institute of Electrical and Electronics Engineers, New York, 1982).
[Crossref]

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]

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 9, 521–534 (1981).
[Crossref]

Julesz, B.

Lowry, E. M.

J. J. DePalma, E. M. Lowry, “Sine-wave response of the visual system,”J. Opt. Soc. Am. 228, 328–335 (1962).
[Crossref]

Marcelja, S.

Metz, C. E.

H.-P. Chan, C. E. Metz, K. Doi, “Digital image processing: optimal spatial filter for maximization of the perceived SNR based on a statistical decision theory model for the human observer,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 2–11 (1985).
[Crossref]

D. J. Goodenough, C. E. Metz, “Implications of a noisy observer to data processing techniques,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 400–419.

Mostafavi, H.

H. Mostafavi, D. Sakrison, “Structure and properties of a single channel in the human visual system,” Vision Res. 16, 957–968 (1976).
[Crossref] [PubMed]

Myers, K. J.

Nachmias, J.

J. Nachmias, B. E. Rogowitz, “Masking by spatially modulated gratings,” Vision Res. 23, 1621–1629 (1983).
[Crossref]

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single channel and multichannels models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

M. Sachs, J. Nachmias, J. Robson, “Spatial-frequency channels in human vision,”J. Opt. Soc. Am. 61, 1176–1186 (1971).
[Crossref] [PubMed]

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

Patton, D. D.

Pelli, D. G.

D. G. Pelli, “Effects of visual noise,” doctoral dissertation (Cambridge University, Cambridge, 1980).

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 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 15–19.

Robson, J.

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

Rogowitz, B. E.

J. Nachmias, B. E. Rogowitz, “Masking by spatially modulated gratings,” Vision Res. 23, 1621–1629 (1983).
[Crossref]

Rosenbruch, K. J.

K. J. Rosenbruch, “The contrast sensitivity of the eye as a factor in the evaluation of optical images,” Optik 16, 135–45 (1959).

Sachs, M.

Sakrison, D.

H. Mostafavi, D. Sakrison, “Structure and properties of a single channel in the human visual system,” Vision Res. 16, 957–968 (1976).
[Crossref] [PubMed]

Schade, O. H.

O. H. Schade, “Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems,”RCA Rev. 9, 5–37 (1948).

Seeley, G. W.

Strohmeyer, C. F.

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]

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 9, 521–534 (1981).
[Crossref]

Swets, J. A.

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

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

Todd-Pokropek, A. E.

S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 15–19.

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.

Wagner, R. F.

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[Crossref]

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 the International Workshop on Physics and Engineering in Medical Images, O. Nalcioglu, J. M. S. Prewitt, eds. (Institute of Electrical and Electronics Engineers, New York, 1982).
[Crossref]

Watson, A. B.

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983).
[Crossref]

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]

J. IEE (London) (1)

D. Gabor, “Theory of communication,” J. IEE (London) 93, 429–457 (1946).

J. Opt. Soc. Am. (5)

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

J. Physiol. (London) (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,”J. Physiol. (London) 197, 551–566 (1968).

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]

Optik (1)

K. J. Rosenbruch, “The contrast sensitivity of the eye as a factor in the evaluation of optical images,” Optik 16, 135–45 (1959).

Percept. Psychophys. (1)

R. G. Swensson, P. F. Judy, “Detection of noisy visual targets: models for the effects of spatial uncertainty and signal-to-noise ratio,” Percept. Psychophys. 9, 521–534 (1981).
[Crossref]

Phys. Med. Biol. (3)

M. S. Chesters, G. A. Hay, “Quantitative relation between detectability and noise power,” Phys. Med. Biol. 28, 1113–1125 (1983).
[Crossref]

R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
[Crossref]

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]

RCA Rev. (1)

O. H. Schade, “Electro-optical characteristics of television systems. I. Characteristics of vision and visual systems,”RCA Rev. 9, 5–37 (1948).

Vision Res. (6)

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

N. Graham, J. Nachmias, “Detection of grating patterns containing two spatial frequencies: a comparison of single channel and multichannels models,” Vision Res. 11, 251–259 (1971).
[Crossref] [PubMed]

H. Mostafavi, D. Sakrison, “Structure and properties of a single channel in the human visual system,” Vision Res. 16, 957–968 (1976).
[Crossref] [PubMed]

J. D. Daugman, “Two-dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1982).
[Crossref]

G. B. Henning, B. G. Hertz, D. E. Broadbent, “Some experiments bearing on the hypothesis that the visual system analyzes spatial patterns in independent bands of spatial frequency,” Vision Res. 15, 887–897 (1975).
[Crossref]

J. Nachmias, B. E. Rogowitz, “Masking by spatially modulated gratings,” Vision Res. 23, 1621–1629 (1983).
[Crossref]

Other (14)

M. Halter, “On the spatial breadth of spatial frequency channels in human visual detection,” doctoral dissertation (University of California, Berkeley, Calif., 1976).

A. B. Watson, “Detection and recognition of simple spatial forms,” in Physical and Biological Processing of Images, O. J. Braddick, A. C. Sleigh, eds. (Springer-Verlag, New York, 1983).
[Crossref]

K. J. Myers, “Visual perception in correlated noise,” doctoral dissertation (University of Arizona, Tucson, Ariz., 1985).

H.-P. Chan, C. E. Metz, K. Doi, “Digital image processing: optimal spatial filter for maximization of the perceived SNR based on a statistical decision theory model for the human observer,” in Application of Optical Instrumentation in Medicine XIII: Medical Image Production, Processing, and Display, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.535, 2–11 (1985).
[Crossref]

A. E. Burgess, “On observer internal noise,” in Application of Optical Instrumentation in Medicine XIV and Picture Archiving and Communication Systems, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.626, 208–213 (1986).
[Crossref]

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, New York, 1965).

H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vols. 1–3.

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

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

D. J. Goodenough, C. E. Metz, “Implications of a noisy observer to data processing techniques,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 400–419.

D. G. Pelli, “Effects of visual noise,” doctoral dissertation (Cambridge University, Cambridge, 1980).

S. M. Pizer, A. E. Todd-Pokropek, “Noise character in processed scintigrams,” in Proceedings of the 4th International Conference on Information Processing in Scintigraphy, C. Raynaud, A. Todd-Pokropek, eds. (Commissariat à l’Energie Atomique, Orsay, France, 1975), pp. 15–19.

A. E. Burgess, R. F. Wagner, R. J. Jennings, “Human signal detection performance for noisy medical images,” in Proceedings of the International Workshop on Physics and Engineering in Medical Images, O. Nalcioglu, J. M. S. Prewitt, eds. (Institute of Electrical and Electronics Engineers, New York, 1982).
[Crossref]

A. E. Burgess, “Statistical efficiency of perceptual decisions,” in Application of Optical Instrumentation in Medicine XII: Medical Image Production, Processing, Display, and Archiving, R. H. Schneider, S. J. Dwyer, eds., Proc. Soc. Photo-Opt. Instrum. Eng.454, 18–26 (1984).
[Crossref]

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Figures (11)

Fig. 1
Fig. 1

Model of visual system including frequency-selective channels proposed by Sachs et al.14

Fig. 2
Fig. 2

Model of an ideal observer constrained to process visual stimuli through frequency-selective channels before evaluating the likelihood ratio.

Fig. 3
Fig. 3

Model of the imaging system used to generate simulated images. The object array is convolved with the first point-spread function, and then white noise is added to the data. The second point-spread function serves to correlate the noise in the final image.

Fig. 4
Fig. 4

Comparison of SNR values for nonprewhitening ideal observer (✦) with those for a channelized ideal observer for detection of a low-contrast disk in correlated noise. The parameter n specifies the noise correlation. SNR values for a channelized ideal observer are shown for the following values of α and ρc, the width and cut-on frequency of the channels, respectively: ○, 1.5, 1.5; ●, 1.5, 2.0; △, 2.0, 1.5; ▲, 2.0, 2.0.

Fig. 5
Fig. 5

Plot of the disk object spectrum and the overall system transfer function (system TF) versus the spatial frequency. Also shown is the square of the transfer function that is responsible for the noise correlation (for n = 4). The vertical bars show the boundaries between the numbered frequency channels. The channelized ideal observer does not utilize any frequency information below ρc.

Fig. 6
Fig. 6

Profiles of the ramp-edged disk and Gaussian objects normalized to have equal underlying areas.

Fig. 7
Fig. 7

The amplitude of the difference spectrum for the ramp-edged disk and Gaussian objects versus the spatial frequency in pixels. Unlike the disk-detection experiment, in which the difference spectrum was peaked at zero spatial frequency, this discrimination task corresponds to a difference spectrum that is zero at zero spatial frequency.

Fig. 8
Fig. 8

SNR values for channelized ideal observers and nonprewhitening ideal observers for the disk-versus-Gaussian-discrimination task. Symbols are as described for Fig. 4.

Fig. 9
Fig. 9

Object profiles for a size-discrimination task, using two ramp-edged disks of different diameters (DIAM.).

Fig. 10
Fig. 10

Difference spectrum for the size-discrimination objects. These objects were also normalized to give zero difference spectrum at zero spatial frequency.

Fig. 11
Fig. 11

SNR values for channelized ideal observers and nonprewhitening ideal observers (✦) for the size-discrimination task. Symbols are as described for Fig. 4.

Equations (67)

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H 1 : r _ = s 1 + n _ , H 2 : r _ = s 2 + n _ .
H 1 : R _ = F r _ = S 1 + N _ , H 2 : R _ = F r _ = S 2 + N _ .
V _ k = U k · R _ + M _ k ,
V _ = U R _ + M _ .
V _ H i = U R _ H i + M _ H i = U S i ,
K i = ( V _ - V ¯ i ) ( V _ - V ¯ i ) H i ,
K = U NN _ U + MM _ = U W N U + W M .
p ( V _ H i ) = [ ( 2 π ) N K ] - 1 / 2 exp [ - ½ ( V _ - V ¯ i ) K - 1 ( V _ - V ¯ i ) ] .
Λ _ ( V _ ) = p ( V _ H 2 ) p ( V _ H 1 )
Λ _ ( V _ ) = exp [ - ½ ( V _ - V ¯ 2 ) K - 1 ( V _ - V ¯ 2 ) ] exp [ - ½ ( V _ - V ¯ 1 ) K - 1 ( V _ - V ¯ 1 ) ] .
λ _ ( V _ ) = ln Λ _ ( V _ ) = - ½ ( V _ - V ¯ 2 ) K - 1 ( V _ - V ¯ 2 ) + ½ ( V _ - V ¯ 1 ) K - 1 ( V _ - V ¯ 1 ) .
λ _ ( V _ ) = ½ [ { V ¯ 2 - V ¯ 1 } K - 1 V _ ] + ½ [ V _ K - 1 { V ¯ 2 - V ¯ 1 } ] + terms independent of the data .
Choose H 2 if λ _ ( V _ ) > λ c ; otherwise choose H 1 .
½ [ ( V ¯ 2 - V ¯ 1 ) K - 1 V _ + V _ K - 1 ( V ¯ 2 - V ¯ 1 ) ] > λ c ,
V ¯ 2 - V ¯ 1 = U ( S 2 - S 1 ) = U Δ S .
λ _ ( V _ ) = ½ { Δ S U K - 1 V _ + V _ K - 1 U Δ S } .
λ _ ( V _ ) = Δ S U K - 1 V _ .
SNR ideal chan = ( Δ S U K - 1 U Δ S ) 1 / 2 .
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 .
U m = 1 α m - 1 ρ c < ρ < α m ρ c = 0 otherwise ,
( SNR ideal chan ) 2 = m = 1 L [ 2 π α m - 1 ρ c α m ρ c A D ( ρ ) P 1 ( ρ ) P 2 ( ρ ) ρ d ρ ] 2 2 π α m - 1 ρ c α m ρ c N 0 [ P 2 ( ρ ) ] 2 ρ d ρ .
N _ = F n _ ,
K = nn _ T .
p ( n _ ) = [ ( 2 π ) M K ] - 1 / 2 exp ( - ½ n _ T K - 1 n _ ) .
K ˜ NN _ = F K F .
M ( ω ) = exp ( i ω T n _ ) = exp ( - ½ ω T K ω ) ,
Ω = F ω .
Ω N _ = ω T n _ .
M ˜ ( Ω ) = exp ( i Ω N _ ) = exp ( i ω T n _ ) = M ( ω ) = exp ( - ½ ω T K ω ) = exp ( - ½ Ω K ˜ Ω ) .
K ˜ n m = σ ˜ n 2 δ n m .
Ω N _ = n = 0 M - 1 Ω n * N _ n = 2 n = 0 M / 2 - 1 ( Ω n N _ n + Ω n N _ n ) ,
Ω K ˜ Ω = n = 0 M - 1 Ω n 2 σ ˜ n 2 = 2 n = 0 M / 2 - 1 Ω n 2 σ ˜ n 2 ,
M ˜ ( Ω ) = exp ( i Ω N _ ) = exp ( - n = 0 - M / 2 - 1 Ω n 2 σ ˜ n 2 ) = - d N _ 0 - d N _ 0 - d N _ M / 2 - 1 × - d N _ M / 2 - 1 × p ˜ ( N _ ) exp ( 2 i n = 0 M / 2 - 1 ( Ω n N _ n + Ω n N _ n ) ) ,
p ˜ ( N _ ) = [ ( 2 π ) M K ˜ ] - 1 / 2 exp ( - n = 0 M / 2 - 1 N _ n 2 σ n 2 ) ,
K - 1 = F K ˜ - 1 F ,             n _ = F N _ ,             n _ T = N _ F ,
n _ T K - 1 n _ = N _ F F K ˜ - 1 F F N _ = N _ K ˜ - 1 N _ ,
A = F a ,             B = F b ,
F n m = 1 M 1 / 2 exp ( - 2 π i n m / M ) ,
F = F - 1 ,
( F ) n m = ( F m n ) * .
A B = ( F a ) F b = a T F F b = a T b ,
- f ( x ) g * ( x ) d x = - F ( ν ) G * ( ν ) d ν .
A k = A M - k * ,
λ _ H i = Δ S U K - 1 V _ H i = Δ S U K - 1 V _ H i = Δ S U K - 1 ( U S i ) .
m λ = λ _ H 2 - λ _ H 1 = Δ S U K - 1 U S 2 - Δ S U K - 1 U S 1 = Δ S U K - 1 U Δ S .
σ λ 2 = ( λ _ - λ _ H 2 ) 2 H 2 = ( Δ S U K - 1 V _ - Δ S U K - 1 U S 2 ) 2 H 2 = [ Δ S U K - 1 ( U N _ + M _ ) ] 2 H 2 ,
σ λ 2 = [ Δ S U K - 1 ( U N _ + M _ ) ] [ Δ S U K - 1 ( U N _ + M _ ) ] H 2 = [ Δ S U K - 1 ( U N _ + M _ ) ] [ Δ S U K - 1 ( U N _ + M _ ) ] H 2 = Δ S U K - 1 ( U N _ + M _ ) ( U N _ + M _ ) H 2 K - 1 U Δ S .
( U N _ + M _ ) ( U N _ + M _ ) = U NN _ U + MM _
σ λ 2 = Δ S U K - 1 U Δ S .
SNR ideal chan = λ _ H 2 - λ _ H 1 σ λ = [ Δ S U K - 1 U Δ S ] 1 / 2 .
K = U W N U + W M ,
W N = NN _ = F nn _ F = F C n F
W M = MM _ .
[ W N ] n m = δ n m η m .
[ U W N U ] n m = j = 1 J k = 1 J U n j [ W N ] j k U k m = k = 1 J U n k η k U m k * .
[ U W N U ] n m = U n ( ω ) W N ( ω ) U m * ( ω ) d ω .
[ U W N U ] n m = U [ ω n - ω ω n ] W N ( ω ) U * [ ω m - ω ω m ] d ω .
[ U W N U ] n m = δ n m | U [ ω m - ω ω m ] | 2 W N ( ω ) d ω .
[ U W N U ] n m = δ n m η m .
[ W M ] n m = δ n m μ m .
[ K - 1 ] n m = δ n m [ η + μ ] m - 1 .
( SNR ideal chan ) 2 = Δ S U K - 1 U Δ S = n = 1 L m = 1 L [ ( U Δ S ) ] n [ K - 1 ] n m [ ( U Δ S ) ] m .
( SNR ideal chan ) 2 = n = 1 L m = 1 L [ ( U Δ S ) ] n [ ( U Δ S ) ] m δ n m [ η + μ ] m = m = 1 L U Δ S m 2 [ η + μ ] m .
U m = 1 α m - 1 ρ c < ρ < α m ρ c = 0 otherwise .
( SNR ideal chan ) 2 = m = 1 L [ 2 π α m - 1 ρ c α m ρ c A D ( ρ ) P 1 ( ρ ) P 2 ( ρ ) ρ d ρ ] 2 2 π α m - 1 ρ c α m ρ c N 0 [ P 2 ( ρ ) ] 2 ρ d ρ .

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