Abstract

Image quality can be objectively defined according to how well an observer can perform a task of practical interest given the image. We review a practical model observer for the signal-detection task. The ideal observer for this task is a function of the image probability distributions, which are multidimensional and complicated. This observer is often too difficult to derive or estimate. An alternative to the ideal observer is the ideal linear observer, which can still be unmanageable. Our alternative is the ideal linear observer constrained to a small set of channels: the channelized-Hotelling observer.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  39. J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  42. H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
  47. B. D. Gallas, “Variance of the channelized-Hotelling observer from a finite number of trainers and testers,” in Medical Imaging, 2003: Image Perception, Observer Performance, and Technology Assessment, D. P. Chakraborty, E. A. Krupinski, eds., Proc. SPIE5034, 100–111 (2003).
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2002 (1)

2001 (1)

1999 (1)

1997 (1)

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

1995 (2)

D. G. Brown, M. F. Insana, M. Tapiovaara, “Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. fisher information, fourier crosstalk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

1992 (2)

J. P. Rolland, H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
[CrossRef] [PubMed]

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

1990 (2)

1989 (1)

K. Fukunaga, R. R. Hayes, “Effects of sample size in classifier design,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 873–885 (1989).
[CrossRef]

1987 (1)

1981 (1)

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

1979 (1)

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[CrossRef] [PubMed]

1977 (1)

H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1977).
[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) (also appeared in Refs. 14 and 16).
[CrossRef]

1948 (1)

1946 (1)

J. H. Van Vleck, D. Middleton, “A theoretical comparison of the visual, aural, and meter reception of pulsed signals in the presence of noise,” J. Appl. Phys. 17, 940–971 (1946).
[CrossRef]

1943 (1)

D. O. North, “An analysis of factors which determine signal-noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1943) [reprinted in Proc. IRE 51, 1016–1028 (1963)].
[CrossRef]

1936 (1)

R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Ann Eugen. 7, 179–188 (1936).
[CrossRef]

1931 (1)

H. Hotelling, “The generalization of Student’s ratio,” Ann. Math. Stat. 2, 360–378 (1931).
[CrossRef]

Abbey, C. K.

C. K. Abbey, H. H. Barrett, “Human and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473–488 (2001).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Practical guide to model observers for visual detection in synthetic and natural noisy images,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 629–654.

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs. model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Processing, H. L. Kundel, ed., Proc. SPIE3340, 16–26 (1998).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Andrews, H. C.

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

Barlow, H. B.

A. E. Burgess, R. J. Jennings, R. F. Wagner, H. B. Barlow, “Efficiency of human visual 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 (1977).
[CrossRef]

Barrett, H.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Barrett, H. H.

E. Clarkson, M. A. Kupinski, H. H. Barrett, “Transformation of characteristic functionals through imaging systems,” Opt. Express 10, 536–539 (2002).
[CrossRef] [PubMed]

C. K. Abbey, H. H. Barrett, “Human and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473–488 (2001).
[CrossRef]

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. fisher information, fourier crosstalk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

J. P. Rolland, H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
[CrossRef] [PubMed]

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

H. H. Barrett, “Objective assessment of image quality: effects of quantum noise and object variability,” J. Opt. Soc. Am. A 7, 1266–1278 (1990).
[CrossRef] [PubMed]

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[CrossRef] [PubMed]

K. J. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
[CrossRef] [PubMed]

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, San Diego, Calif., 1981).

H. H. Barrett, C. K. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

H. H. Barrett, K. J. Myers, Foundations of Image Science (to be published).

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) (also appeared in Refs. 14 and 16).
[CrossRef]

Bochud, F. O.

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Practical guide to model observers for visual detection in synthetic and natural noisy images,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 629–654.

Bodano, A.

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

Boswell, J. S.

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

Brown, D. G.

D. G. Brown, M. F. Insana, M. Tapiovaara, “Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

Burgess, A. E.

A. E. Burgess, “Visual signal detection with two-component noise: low-pass spectrum effects,” J. Opt. Soc. Am. A 16, 694–704 (1999).
[CrossRef]

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

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

Castleman, K. R.

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1979).

Clarkson, E.

E. Clarkson, M. A. Kupinski, H. H. Barrett, “Transformation of characteristic functionals through imaging systems,” Opt. Express 10, 536–539 (2002).
[CrossRef] [PubMed]

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

Cohn, D. L.

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

Creelman, C. D.

N. A. MacMillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Denny, J. L.

DeVries, D. J.

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

Dougherty, D.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Eckstein, M.

H. H. Barrett, C. K. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Eckstein, M. P.

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs. model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Processing, H. L. Kundel, ed., Proc. SPIE3340, 16–26 (1998).
[CrossRef]

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Practical guide to model observers for visual detection in synthetic and natural noisy images,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 629–654.

Faris, S.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Fisher, R. A.

R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Ann Eugen. 7, 179–188 (1936).
[CrossRef]

Fukunaga, K.

K. Fukunaga, R. R. Hayes, “Effects of sample size in classifier design,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 873–885 (1989).
[CrossRef]

K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed. (Academic, New York, 1990).

Gagne, R. M.

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

Gallas, B.

H. H. Barrett, C. K. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Gallas, B. D.

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

B. D. Gallas, “Variance of the channelized-Hotelling observer from a finite number of trainers and testers,” in Medical Imaging, 2003: Image Perception, Observer Performance, and Technology Assessment, D. P. Chakraborty, E. A. Krupinski, eds., Proc. SPIE5034, 100–111 (2003).
[CrossRef]

Gindi, G.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Girodias, K.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

Goldman, S.

S. Goldman, Information Theory (Prentice-Hall, New York, 1953).

Gooley, T.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966) [reprint (Krieger, New York, 1974)].

Guedon, J. P.

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

Hanson, K. M.

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[CrossRef] [PubMed]

Hayes, R. R.

K. Fukunaga, R. R. Hayes, “Effects of sample size in classifier design,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 873–885 (1989).
[CrossRef]

Hotelling, H.

H. Hotelling, “The generalization of Student’s ratio,” Ann. Math. Stat. 2, 360–378 (1931).
[CrossRef]

Hsiao, I. T.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Hunt, B. R.

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

Hutton, D. A.

D. A. Hutton, R. N. Strickland, “Channelized detection filters for detecting tumors in nuclear medical images,” in Medical Imaging 1997: Image Processing, K. M. Hanson, ed., Proc. SPIE3034, 457–466 (1997).
[CrossRef]

Insana, M. F.

D. G. Brown, M. F. Insana, M. Tapiovaara, “Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

Jennings, R. J.

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

King, M. A.

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

Kupinski, M. A.

Li, X.

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

MacMillan, N. A.

N. A. MacMillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

Melsa, J. L.

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

Metz, C. E.

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

C. E. Metz, “Fundamental ROC analysis,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 751–769.

Middleton, D.

J. H. Van Vleck, D. Middleton, “A theoretical comparison of the visual, aural, and meter reception of pulsed signals in the presence of noise,” J. Appl. Phys. 17, 940–971 (1946).
[CrossRef]

Myers, K. J.

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. fisher information, fourier crosstalk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[CrossRef] [PubMed]

K. J. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
[CrossRef] [PubMed]

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

H. H. Barrett, K. J. Myers, Foundations of Image Science (to be published).

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

North, D. O.

D. O. North, “An analysis of factors which determine signal-noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1943) [reprinted in Proc. IRE 51, 1016–1028 (1963)].
[CrossRef]

Pickett, R. M.

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

Rolland, J.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

Rolland, J. P.

Rose, A.

Soares, E. J.

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

Strickland, R. N.

D. A. Hutton, R. N. Strickland, “Channelized detection filters for detecting tumors in nuclear medical images,” in Medical Imaging 1997: Image Processing, K. M. Hanson, ed., Proc. SPIE3034, 457–466 (1997).
[CrossRef]

Swets, J. A.

J. A. Swets, Signal Detection and Recognition by Human Observers: Contemporary Readings (Wiley, New York, 1964).

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966) [reprint (Krieger, New York, 1974)].

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, San Diego, Calif., 1981).

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) (also appeared in Refs. 14 and 16).
[CrossRef]

Tapiovaara, M.

D. G. Brown, M. F. Insana, M. Tapiovaara, “Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

Tsui, B. M. W.

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

Van Trees, H. L.

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

Van Vleck, J. H.

J. H. Van Vleck, D. Middleton, “A theoretical comparison of the visual, aural, and meter reception of pulsed signals in the presence of noise,” J. Appl. Phys. 17, 940–971 (1946).
[CrossRef]

Wagner, R. F.

H. H. Barrett, J. L. Denny, R. F. Wagner, K. J. Myers, “Objective assessment of image quality. II. fisher information, fourier crosstalk, and figures of merit for task performance,” J. Opt. Soc. Am. A 12, 834–852 (1995).
[CrossRef]

K. J. Myers, J. P. Rolland, H. H. Barrett, R. F. Wagner, “Aperture optimization for emission imaging: effect of a spatially varying background,” J. Opt. Soc. Am. A 7, 1279–1293 (1990).
[CrossRef] [PubMed]

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

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

Wald, A.

A. Wald, Statistical Decision Functions (Wiley, New York, 1950).

Wear, K. A.

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

White, T.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

Whiting, J. S.

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs. model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Processing, H. L. Kundel, ed., Proc. SPIE3340, 16–26 (1998).
[CrossRef]

Wilson, D.

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

Yao, J.

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

Zhang, H.

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

Ann Eugen. (1)

R. A. Fisher, “The use of multiple measurements in taxonomic problems,” Ann Eugen. 7, 179–188 (1936).
[CrossRef]

Ann. Math. Stat. (1)

H. Hotelling, “The generalization of Student’s ratio,” Ann. Math. Stat. 2, 360–378 (1931).
[CrossRef]

IEEE Trans. Nucl. Sci. (1)

D. J. DeVries, M. A. King, E. J. Soares, B. M. W. Tsui, C. E. Metz, “Evaluation of the effect of scatter correction on lesion detection in hepatic SPECT imaging,” IEEE Trans. Nucl. Sci. 44, 1733–1740 (1997).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

K. Fukunaga, R. R. Hayes, “Effects of sample size in classifier design,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 873–885 (1989).
[CrossRef]

Image Vision Comput. (1)

H. H. Barrett, T. Gooley, K. Girodias, J. Rolland, T. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
[CrossRef]

J. Acoust. Soc. Am. (2)

D. G. Brown, M. F. Insana, M. Tapiovaara, “Detection performance of the ideal decision function and its McLaurin expansion: signal position unknown,” J. Acoust. Soc. Am. 97, 379–398 (1995).
[CrossRef] [PubMed]

W. P. Tanner, T. G. Birdsall, “Definitions of d′ and η as psychophysical measures,” J. Acoust. Soc. Am. 30, 922–928 (1958) (also appeared in Refs. 14 and 16).
[CrossRef]

J. Appl. Phys. (1)

J. H. Van Vleck, D. Middleton, “A theoretical comparison of the visual, aural, and meter reception of pulsed signals in the presence of noise,” J. Appl. Phys. 17, 940–971 (1946).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (7)

Med. Phys. (1)

K. M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6, 441–451 (1979).
[CrossRef] [PubMed]

Opt. Express (1)

Proc. IEEE (1)

D. O. North, “An analysis of factors which determine signal-noise discrimination in pulsed carrier systems,” Proc. IEEE 51, 1016–1027 (1943) [reprinted in Proc. IRE 51, 1016–1028 (1963)].
[CrossRef]

Science (1)

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

Vision Res. (1)

H. B. Barlow, “The efficiency of detecting changes in density in random dot patterns,” Vision Res. 18, 637–650 (1977).
[CrossRef]

Other (27)

T. E. Cohn, ed., Visual Detection, Vol. 3 of OSA Collected Works in Optics Series (Optical Society of America, Washington, D.C., 1993).

J. A. Swets, Signal Detection and Recognition by Human Observers: Contemporary Readings (Wiley, New York, 1964).

C. E. Metz, “Fundamental ROC analysis,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 751–769.

R. F. Wagner, D. G. Brown, J. P. Guedon, K. J. Myers, K. A. Wear, “Multivariate Gaussian pattern classification: effects of finite sample size and the addition of correlated or noisy features on summary measures of goodness,” in Information Processing in Medical Imaging: Proceeding of the 13th International Conference (IPMI ’93), H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, New York, 1993), pp. 507–524.

A. Wald, Statistical Decision Functions (Wiley, New York, 1950).

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Wiley, New York, 1966) [reprint (Krieger, New York, 1974)].

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

K. Fukunaga, Introduction to Statistical Pattern Recognition, 2nd ed. (Academic, New York, 1990).

J. L. Melsa, D. L. Cohn, Decision and Estimation Theory (McGraw-Hill, New York, 1978).

J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems: Methods from Signal Detection Theory (Academic, New York, 1982).

N. A. MacMillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, UK, 1991).

S. Goldman, Information Theory (Prentice-Hall, New York, 1953).

K. R. Castleman, Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1979).

M. P. Eckstein, C. K. Abbey, J. S. Whiting, “Human vs. model observers in anatomic backgrounds,” in Medical Imaging 1998: Image Processing, H. L. Kundel, ed., Proc. SPIE3340, 16–26 (1998).
[CrossRef]

D. A. Hutton, R. N. Strickland, “Channelized detection filters for detecting tumors in nuclear medical images,” in Medical Imaging 1997: Image Processing, K. M. Hanson, ed., Proc. SPIE3034, 457–466 (1997).
[CrossRef]

H. H. Barrett, C. K. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging 1998: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

S. Faris, D. Wilson, H. Barrett, D. Dougherty, G. Gindi, I. T. Hsiao, “Using a digital anatomical phantom to opti-mize an imaging system,” in Medical Imaging 1999: Physics of Medical Imaging, J. M. Boone, J. T. Dobbins, eds., Proc. SPIE3659, 98–106 (1999).
[CrossRef]

J. S. Boswell, A. Bodano, R. M. Gagne, B. D. Gallas, K. J. Myers, “Assessment of lesion detectability by Monte Carlo modeling of digital radiography systems,” in Medical Imaging 2002: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffe, eds., Proc. SPIE4682, 665–674 (2002).
[CrossRef]

H. H. Barrett, K. J. Myers, B. D. Gallas, E. Clarkson, H. Zhang, “Megalopinakophobia: its symptoms and cures,” in Medical Imaging 2001: Physics of Medical Imaging, L. E. Antonuk, M. J. Yaffee, eds., Proc. SPIE4320, 299–307 (2001).
[CrossRef]

H. H. Barrett, K. J. Myers, Foundations of Image Science (to be published).

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

H. H. Barrett, W. Swindell, Radiological Imaging: The Theory of Image Formation, Detection, and Processing (Academic, San Diego, Calif., 1981).

M. P. Eckstein, C. K. Abbey, F. O. Bochud, “Practical guide to model observers for visual detection in synthetic and natural noisy images,” in Handbook of Medical Imaging. Vol. 1: Physics and Psychophysics, J. Beutel, H. L. Kundel, R. L. Van Metter, eds. (SPIE Press, Bellingham, Wash., 2000), pp. 629–654.

B. D. Gallas, “Variance of the channelized-Hotelling observer from a finite number of trainers and testers,” in Medical Imaging, 2003: Image Perception, Observer Performance, and Technology Assessment, D. P. Chakraborty, E. A. Krupinski, eds., Proc. SPIE5034, 100–111 (2003).
[CrossRef]

International Commission on Radiation Units and Measurements, “Medical imaging: the assessment of image quality,” (International Commission on Radiation Units and Measurements, Bethesda, Md., 1996).

R. F. Wagner, D. G. Brown, C. E. Metz, “On the multiplex advantage of coded source/aperture photon imaging,” in Digital Radiography, W. R. Brody, ed., Proc. SPIE314, 72–76 (1981).
[CrossRef]

A. E. Burgess, X. Li, C. K. Abbey, “Nodule detection in two component noise: toward patient structure,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 2–13 (1997).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Examples of LG functions.

Fig. 2
Fig. 2

Gaussian, circle, and besinc lumps smoothed by a Gaussian point-spread function with σh=5 mm representing the imaging system H.

Fig. 3
Fig. 3

In the left column are sample long-exposure (T=75 s) G-like Gaussian (top), circle (middle), and besinc (bottom) lumpy-background images with Poisson noise. These images have an average of 50 broad lumps and a significant background. In the right column are the corresponding gray-level histograms.

Fig. 4
Fig. 4

In the left column are sample long-exposure (T=75 s) P-like Gaussian (top), circle (middle), and besinc (bottom) lumpy-background images with Poisson noise. These images have an average of ten narrow lumps and a moderate background. In the right column are the corresponding gray-level histograms.

Fig. 5
Fig. 5

Plots of estimated SNRs as a function of number of channels. Each curve is the performance of an LG ch-Hotelling observer with a different σu. There were 3000 pairs of images used for training and 3000 pairs of images used for testing.

Fig. 6
Fig. 6

SNRI of the dft-Hotelling observer based on different detector sizes and 1-mm×1-mm pixels. The results for smaller pixels (Δ=0.50 and 0.25 mm) are identical to those here.

Fig. 7
Fig. 7

Templates of the high-exposure P-like circle lumpy background. In the top half of this image is the template of the default dft-Hotelling observer, in the bottom-left quadrant is the template of the ch-Hotelling observer, and in the bottom-right quadrant is the template of the nonpixelized ideal linear observer. Artifacts in the top corners of the default dft-Hotelling template are caused by the insufficient sampling by the default grid.

Fig. 8
Fig. 8

Estimated SNRs of the default ch-Hotelling observer (solid symbols) and the default dft-Hotelling observer (open symbols) versus SNRI of the continuous ideal linear observer. For a given lump type, exposure time increases from left to right. The vertical dotted lines in each mark the results for the medium-exposure circle lumpy backgrounds. The circles to the left correspond to the low-exposure results, and the circles to the right correspond to the high-exposure results.

Tables (1)

Tables Icon

Table 1 Definitions of Lump Functions

Equations (56)

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

SNRτ=τ|H1-τ|H0[12var(τ|H1)+12var(τ|H0)]1/2.
SNRw=wtswtCgw,
s=g¯1-g¯0,
g¯m=g|Hmform=0, 1,
Cg=12m=01(g-g¯m)(g-g¯m)t|Hm.
wg=Cg-1s,
SNRI=wgts(wgtCgwg)1/2
=stCg-1s(stCg-1CgCg-1s)1/2
=(stCg-1s)1/2.
U=[u1, u2,, uJ].
vj=i=1N[uj]igi=(uj)tg,
wv=Cv-1sv.
sv=Uts,
Cv=UtCgU.
tv(v)=(sv)tCv-1vt(g)=stU(UtCgU)-1Utg.
wg=j=1Jujaj=Ua
τ=(wg)tg=atUtg=atv.
Lj(x)=j=0j(-1)jjjxjj!,
L0(x)=1,
L1(x)=-x+1,
L2(x)=12! (x2-4x+2),
L3(x)=13! (-x3+9x2-18x+6),
L4(x)=14! (x4-16x3+72x2-96x+24).
0dx exp(-x)Lj(x)Lj(x)=δj,j.
12π02πdθ04πrdrau2exp(-2πr2/au2)
×Lj2πr2au2Lj2πr2au2=δj,j,
uj(r|au)=2auexp-πr2au2Lj2πr2au2.
w(r)=exp-πr2au2j=0αjLj2πr2au2,
αj=d2ruj(r)w(r).
Δg(r)Δg(r-r0)=R(r, r-r0)R(r0),
t(g)=-d2rw(r)g(r).
-d2rR(r-r)wg(r)=s(-r),
Cgwg=s.
R˜(ρ)w˜g(ρ)=s˜c(ρ),
w˜g(ρ)=s˜c(ρ)R˜(ρ).
[Cg]ii=[R]i-i,
i=(1,1)(M,M)[R]i-i[wg]i=si,
[Cg]ii=[R][i-i]M,
wdft=Cdft-1s.
[Hf]i=T[h * f](ri)=Td2rh(r-ri)f(r).
p(g|Hf)=i=(1,1)(M,M)p(gi|Hf)
=i=(1,1)(M,M)exp(-[Hf]i)[Hf]igigi!.
b(r)=Ab+k=1l(r-rk).
p({rk}|K)=k=1Kp(rk|K),
p(rk|K)=1L2.
g¯¯i=gig|ff=TIh(Ab+γIl),
Ih=d2rh(r),
Il=d2rl(r).
[Cg]i,i=(gi-g¯¯i)(gi-g¯¯i)g|ff=TIh(Ab+γIl)δi,i+γT2[h*[ll]*h](ri-ri).
SNRw2=(wts)2wtCgw?stCg-1s=SNRI2.
(wts)2?(wtCgw)(stCg-1s).
(wts)2=(wtCg1/2Cg-1/2s)2=[(Cg1/2w)t(Cg-1/2s)]2.
(wts)2Cg1/2w2Cg-1/2s2.
(wts)2(Cg1/2w)t(Cg1/2w)(Cg-1/2s)t(Cg-1/2s).
(wts)2wt[(Cg1/2)tCg1/2]wst[(Cg-1/2)tCg-1/2]s.
(wts)2(wtCgw)(stCg-1s).

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