Abstract

Figures of merit for image quality are derived on the basis of the performance of mathematical observers on specific detection and estimation tasks. The tasks include detection of a known signal superimposed on a known background, detection of a known signal on a random background, estimation of Fourier coefficients of the object, and estimation of the integral of the object over a specified region of interest. The chosen observer for the detection tasks is the ideal linear discriminant, which we call the Hotelling observer. The figures of merit are based on the Fisher information matrix relevant to estimation of the Fourier coefficients and the closely related Fourier crosstalk matrix introduced earlier by Barrett and Gifford [ Phys. Med. Biol. 39, 451 ( 1994)]. A finite submatrix of the infinite Fisher information matrix is used to set Cramer–Rao lower bounds on the variances of the estimates of the first N Fourier coefficients. The figures of merit for detection tasks are shown to be closely related to the concepts of noise-equivalent quanta (NEQ) and generalized NEQ, originally derived for linear, shift-invariant imaging systems and stationary noise. Application of these results to the design of imaging systems is discussed.

© 1995 Optical Society of America

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  1. G. E. Backus, J. F. Gilbert, “Numerical application of a formalism for geophysical inverse problems,” Geophys. J. R. Astron. Soc. 13, 247–276 (1967).
    [CrossRef]
  2. M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
    [CrossRef]
  3. R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
    [CrossRef]
  4. R. F. Wagner, D. G. Brown, “Unified SNR analysis of medical imaging systems,” Phys. Med. Biol. 30, 489–518 (1985).
    [CrossRef]
  5. A. E. Burgess, R. F. Wagner, R. J. Jennings, H. B. Barlow, “Efficiency of human visual discrimination,” Science 214, 93–94 (1981).
    [CrossRef] [PubMed]
  6. J. A. Swets, “Measuring the accuracy of diagnostic systems,” Science 240, 1285–1293 (1988);J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
    [CrossRef] [PubMed]
  7. K. M. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI (Atlanta), G. D. Fullerton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.419, 60–67 (1983).
    [CrossRef]
  8. K. M. Hanson, “Optimization for object localization of the constrained algebraic reconstruction technique,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 146–153 (1989).
    [CrossRef]
  9. S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).
  10. M. F. Kijewski, “The Barankin bound: a model of detection with location uncertainty,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 153–160 (1992).
    [CrossRef]
  11. B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
    [CrossRef] [PubMed]
  12. C. F. Metz, “ROC methodology in radiologic imaging,” Invest. Radiol. 21, 720–733 (1986).
    [CrossRef] [PubMed]
  13. W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am. A 3, 717–725 (1986).
    [CrossRef]
  14. G. T. Herman, K. T. D. Yeung, “Evaluators of image reconstruction algorithms,” Int. J. Imag. Syst. Technol. 1, 187–195 (1989).
    [CrossRef]
  15. G. T. Herman, D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography,” IEEE Trans. Med. Imag. 10, 336–346 (1991).
    [CrossRef]
  16. A. E. Hero, L. Shao, “Information analysis of single photon computed tomography with count losses,” IEEE Trans. Med. Imag. 9, 117–127 (1990).
    [CrossRef]
  17. H. H. Barrett, T. A. Gooley, K. A. Girodias, J. P. Rolland, T. A. White, J. Yao, “Linear discriminants and image quality,” Image Vision Comput. 10, 451–460 (1992).
    [CrossRef]
  18. 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]
  19. 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. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
    [CrossRef]
  20. 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]
  21. J. P. Rolland, “Factors influencing lesion detection in medical imaging,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1990).
  22. 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]
  23. N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).
  24. K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
    [CrossRef]
  25. H. H. Barrett, H. C. Gifford, “Cone–beam tomography with discrete data sets,” Phys. Med. Biol. 39, 451–476 (1994).
    [CrossRef] [PubMed]
  26. H. L. Van Trees, Detection, Estimation, and Modulation Theory (Wiley, New York, 1968), Vol. 1.
  27. K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, San Diego, Calif., 1979).
  28. M. Siotani, T. Hayakawa, Y. Fujikoshi, Modern Multi-variate Statistical Analysis: A Graduate Course and Handbook (American Sciences, Columbus, Ohio, 1985).
  29. H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 219–285.
    [CrossRef]
  30. J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models (Wiley, Bergakademie Freiberg, Germany, 1991).
  31. A. O. Hero, J. A. Fessler, “A fast recursive algorithm for computing CR-type bounds for image reconstruction problems,” presented at the Institute of Electrical and Electronics Engineers Nuclear Science Symposium, Orlando, Fla., October 1992.
  32. R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
    [CrossRef] [PubMed]
  33. H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
    [CrossRef]
  34. 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]
  35. 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]
  36. J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 161–168 (1992).
    [CrossRef]
  37. J. Yao, “Predicting human performance by model observers,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).
  38. A. B. Whalen, Detection of Signals in Noise (Academic, New York, 1971).
  39. R. Shaw, “The equivalent quantum efficiency of the photographic process,” J. Photog. Sci. 11, 199–204 (1963).
  40. R. Shaw, “Evaluating the efficiency of imaging processes,” Rep. Prog. Phys. (UK) 41, 1103–1155 (1978).
    [CrossRef]
  41. J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).
  42. M. J. Tapiovaara, R. F. Wagner, “SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory,” Phys. Med. Biol. 38, 71–92 (1993).
    [CrossRef] [PubMed]
  43. H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
    [CrossRef]
  44. R. G. Paxman, “Coordinated design of restoration algorithm and coded aperture,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1984).
  45. R. G. Paxman, H. H. Barrett, W. E. Smith, T. D. Milster, “Image reconstruction from coded data: code design,” J. Opt. Soc. Am. A 2, 501–509 (1985).
    [CrossRef] [PubMed]
  46. R. A. Horn, “The Hadamard product,” Proc. Symp. Appl. Math. 40, 87–169 (1990).
    [CrossRef]
  47. L. Rade, B. Westergren, Beta Mathematics Handbook (CRC, Boca Raton, Fla., 1989).
  48. H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
    [CrossRef] [PubMed]
  49. D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
    [CrossRef]

1994 (3)

H. H. Barrett, H. C. Gifford, “Cone–beam tomography with discrete data sets,” Phys. Med. Biol. 39, 451–476 (1994).
[CrossRef] [PubMed]

H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
[CrossRef] [PubMed]

D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
[CrossRef]

1993 (2)

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[CrossRef]

M. J. Tapiovaara, R. F. Wagner, “SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory,” Phys. Med. Biol. 38, 71–92 (1993).
[CrossRef] [PubMed]

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

1991 (1)

G. T. Herman, D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography,” IEEE Trans. Med. Imag. 10, 336–346 (1991).
[CrossRef]

1990 (5)

A. E. Hero, L. Shao, “Information analysis of single photon computed tomography with count losses,” IEEE Trans. Med. Imag. 9, 117–127 (1990).
[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]

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

R. A. Horn, “The Hadamard product,” Proc. Symp. Appl. Math. 40, 87–169 (1990).
[CrossRef]

1989 (1)

G. T. Herman, K. T. D. Yeung, “Evaluators of image reconstruction algorithms,” Int. J. Imag. Syst. Technol. 1, 187–195 (1989).
[CrossRef]

1988 (1)

J. A. Swets, “Measuring the accuracy of diagnostic systems,” Science 240, 1285–1293 (1988);J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
[CrossRef] [PubMed]

1987 (2)

1986 (2)

1985 (4)

M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
[CrossRef]

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

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]

R. G. Paxman, H. H. Barrett, W. E. Smith, T. D. Milster, “Image reconstruction from coded data: code design,” J. Opt. Soc. Am. A 2, 501–509 (1985).
[CrossRef] [PubMed]

1981 (1)

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

1978 (2)

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

R. Shaw, “Evaluating the efficiency of imaging processes,” Rep. Prog. Phys. (UK) 41, 1103–1155 (1978).
[CrossRef]

1967 (1)

G. E. Backus, J. F. Gilbert, “Numerical application of a formalism for geophysical inverse problems,” Geophys. J. R. Astron. Soc. 13, 247–276 (1967).
[CrossRef]

1963 (1)

R. Shaw, “The equivalent quantum efficiency of the photographic process,” J. Photog. Sci. 11, 199–204 (1963).

Atkins, F. B.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

Backus, G. E.

G. E. Backus, J. F. Gilbert, “Numerical application of a formalism for geophysical inverse problems,” Geophys. J. R. Astron. Soc. 13, 247–276 (1967).
[CrossRef]

Barber, H. B.

N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).

Barlow, H. B.

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

Barrett, H. H.

H. H. Barrett, H. C. Gifford, “Cone–beam tomography with discrete data sets,” Phys. Med. Biol. 39, 451–476 (1994).
[CrossRef] [PubMed]

H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
[CrossRef] [PubMed]

D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
[CrossRef]

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[CrossRef]

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

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[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]

W. E. Smith, H. H. Barrett, “Hotelling trace criterion as a figure of merit for the optimization of imaging systems,” J. Opt. Soc. Am. A 3, 717–725 (1986).
[CrossRef]

R. G. Paxman, H. H. Barrett, W. E. Smith, T. D. Milster, “Image reconstruction from coded data: code design,” J. Opt. Soc. Am. A 2, 501–509 (1985).
[CrossRef] [PubMed]

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]

H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
[CrossRef]

J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 161–168 (1992).
[CrossRef]

N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 219–285.
[CrossRef]

Beck, R. N.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

Bertero, M.

M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
[CrossRef]

Bibby, J. M.

K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, San Diego, Calif., 1979).

Borgstrom, M. C.

Brown, D. G.

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. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[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. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[CrossRef]

Burgess, A. E.

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

R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[CrossRef]

Dainty, J. C.

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

DeMol, C.

M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
[CrossRef]

Fessler, J. A.

A. O. Hero, J. A. Fessler, “A fast recursive algorithm for computing CR-type bounds for image reconstruction problems,” presented at the Institute of Electrical and Electronics Engineers Nuclear Science Symposium, Orlando, Fla., October 1992.

Fiete, R. D.

Fujikoshi, Y.

M. Siotani, T. Hayakawa, Y. Fujikoshi, Modern Multi-variate Statistical Analysis: A Graduate Course and Handbook (American Sciences, Columbus, Ohio, 1985).

Gifford, H. C.

H. H. Barrett, H. C. Gifford, “Cone–beam tomography with discrete data sets,” Phys. Med. Biol. 39, 451–476 (1994).
[CrossRef] [PubMed]

Gilbert, J. F.

G. E. Backus, J. F. Gilbert, “Numerical application of a formalism for geophysical inverse problems,” Geophys. J. R. Astron. Soc. 13, 247–276 (1967).
[CrossRef]

Girodias, K. A.

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

Gooley, T. A.

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

Hanson, K. M.

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

K. M. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI (Atlanta), G. D. Fullerton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.419, 60–67 (1983).
[CrossRef]

K. M. Hanson, “Optimization for object localization of the constrained algebraic reconstruction technique,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 146–153 (1989).
[CrossRef]

Hartsough, N. E

N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).

Hayakawa, T.

M. Siotani, T. Hayakawa, Y. Fujikoshi, Modern Multi-variate Statistical Analysis: A Graduate Course and Handbook (American Sciences, Columbus, Ohio, 1985).

Herman, G. T.

G. T. Herman, D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography,” IEEE Trans. Med. Imag. 10, 336–346 (1991).
[CrossRef]

G. T. Herman, K. T. D. Yeung, “Evaluators of image reconstruction algorithms,” Int. J. Imag. Syst. Technol. 1, 187–195 (1989).
[CrossRef]

Hero, A. E.

A. E. Hero, L. Shao, “Information analysis of single photon computed tomography with count losses,” IEEE Trans. Med. Imag. 9, 117–127 (1990).
[CrossRef]

Hero, A. O.

A. O. Hero, J. A. Fessler, “A fast recursive algorithm for computing CR-type bounds for image reconstruction problems,” presented at the Institute of Electrical and Electronics Engineers Nuclear Science Symposium, Orlando, Fla., October 1992.

Holman, B. L.

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

Horn, R. A.

R. A. Horn, “The Hadamard product,” Proc. Symp. Appl. Math. 40, 87–169 (1990).
[CrossRef]

Jennings, R. J.

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

Kent, J. T.

K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, San Diego, Calif., 1979).

Kijewski, M. F.

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

M. F. Kijewski, “The Barankin bound: a model of detection with location uncertainty,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 153–160 (1992).
[CrossRef]

Mardia, K. V.

K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, San Diego, Calif., 1979).

Metz, C. E.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[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. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[CrossRef]

Metz, C. F.

C. F. Metz, “ROC methodology in radiologic imaging,” Invest. Radiol. 21, 720–733 (1986).
[CrossRef] [PubMed]

Milster, T. D.

Moore, S. C.

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

Mueller, S. P.

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

Myers, K. J.

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[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]

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “The Hotelling trace criterion and its correlation with human observer performance,” J. Opt. Soc. Am. A 4, 945–953 (1987).
[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]

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]

H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
[CrossRef]

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[CrossRef]

Odhner, D.

G. T. Herman, D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography,” IEEE Trans. Med. Imag. 10, 336–346 (1991).
[CrossRef]

Patton, D. D.

Paxman, R. G.

R. G. Paxman, H. H. Barrett, W. E. Smith, T. D. Milster, “Image reconstruction from coded data: code design,” J. Opt. Soc. Am. A 2, 501–509 (1985).
[CrossRef] [PubMed]

R. G. Paxman, “Coordinated design of restoration algorithm and coded aperture,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1984).

Pike, E. R.

M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
[CrossRef]

Pilz, J.

J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models (Wiley, Bergakademie Freiberg, Germany, 1991).

Rade, L.

L. Rade, B. Westergren, Beta Mathematics Handbook (CRC, Boca Raton, Fla., 1989).

Rolland, J. P.

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[CrossRef]

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

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]

H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
[CrossRef]

J. P. Rolland, “Factors influencing lesion detection in medical imaging,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1990).

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

Seeley, G. W.

Shao, L.

A. E. Hero, L. Shao, “Information analysis of single photon computed tomography with count losses,” IEEE Trans. Med. Imag. 9, 117–127 (1990).
[CrossRef]

Shaw, R.

R. Shaw, “Evaluating the efficiency of imaging processes,” Rep. Prog. Phys. (UK) 41, 1103–1155 (1978).
[CrossRef]

R. Shaw, “The equivalent quantum efficiency of the photographic process,” J. Photog. Sci. 11, 199–204 (1963).

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

Siotani, M.

M. Siotani, T. Hayakawa, Y. Fujikoshi, Modern Multi-variate Statistical Analysis: A Graduate Course and Handbook (American Sciences, Columbus, Ohio, 1985).

Smith, W. E.

Starr, S. J.

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

Swets, J. A.

J. A. Swets, “Measuring the accuracy of diagnostic systems,” Science 240, 1285–1293 (1988);J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
[CrossRef] [PubMed]

Tapiovaara, M. J.

M. J. Tapiovaara, R. F. Wagner, “SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory,” Phys. Med. Biol. 38, 71–92 (1993).
[CrossRef] [PubMed]

R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[CrossRef]

Tsui, B. M. W.

D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
[CrossRef]

H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
[CrossRef] [PubMed]

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

Van Trees, H. L.

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

Wagner, R. F.

M. J. Tapiovaara, R. F. Wagner, “SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory,” Phys. Med. Biol. 38, 71–92 (1993).
[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]

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

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

R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[CrossRef]

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
[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. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[CrossRef]

Westergren, B.

L. Rade, B. Westergren, Beta Mathematics Handbook (CRC, Boca Raton, Fla., 1989).

Whalen, A. B.

A. B. Whalen, Detection of Signals in Noise (Academic, New York, 1971).

White, T. A.

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

Wilson, D. W.

H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
[CrossRef] [PubMed]

D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
[CrossRef]

Woolfenden, J. M.

N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).

Yao, J.

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[CrossRef]

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

J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 161–168 (1992).
[CrossRef]

J. Yao, “Predicting human performance by model observers,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).

Yeung, K. T. D.

G. T. Herman, K. T. D. Yeung, “Evaluators of image reconstruction algorithms,” Int. J. Imag. Syst. Technol. 1, 187–195 (1989).
[CrossRef]

Geophys. J. R. Astron. Soc. (1)

G. E. Backus, J. F. Gilbert, “Numerical application of a formalism for geophysical inverse problems,” Geophys. J. R. Astron. Soc. 13, 247–276 (1967).
[CrossRef]

IEEE Trans. Med. Imag. (2)

G. T. Herman, D. Odhner, “Performance evaluation of an iterative image reconstruction algorithm for positron emission tomography,” IEEE Trans. Med. Imag. 10, 336–346 (1991).
[CrossRef]

A. E. Hero, L. Shao, “Information analysis of single photon computed tomography with count losses,” IEEE Trans. Med. Imag. 9, 117–127 (1990).
[CrossRef]

Image Vision Comput. (1)

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

Int. J. Imag. Syst. Technol. (1)

G. T. Herman, K. T. D. Yeung, “Evaluators of image reconstruction algorithms,” Int. J. Imag. Syst. Technol. 1, 187–195 (1989).
[CrossRef]

Inv. Prob. (1)

M. Bertero, C. DeMol, E. R. Pike, “Linear inverse problems with discrete data. I: General formulation and singular system analysis,” Inv. Prob. 1, 301–330 (1985).
[CrossRef]

Invest. Radiol. (1)

C. F. Metz, “ROC methodology in radiologic imaging,” Invest. Radiol. 21, 720–733 (1986).
[CrossRef] [PubMed]

J. Nucl. Med. (1)

S. P. Mueller, M. F. Kijewski, S. C. Moore, B. L. Holman, “Maximum-likelihood estimation—a model for optimal quantitation in nuclear medicine,” J. Nucl. Med. 31, 1693–1701 (1990).

J. Opt. Soc. Am. A (8)

J. Photog. Sci. (1)

R. Shaw, “The equivalent quantum efficiency of the photographic process,” J. Photog. Sci. 11, 199–204 (1963).

Phys. Med. Biol. (6)

H. H. Barrett, H. C. Gifford, “Cone–beam tomography with discrete data sets,” Phys. Med. Biol. 39, 451–476 (1994).
[CrossRef] [PubMed]

B. M. W. Tsui, C. E. Metz, F. B. Atkins, S. J. Starr, R. N. Beck, “A comparison of optimum spatial resolution in nuclear imaging based on statistical theory and on observer performance,” Phys. Med. Biol. 23, 654–676 (1978).
[CrossRef] [PubMed]

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

M. J. Tapiovaara, R. F. Wagner, “SNR and noise measurements for medical imaging: I. A practical approach based on statistical decision theory,” Phys. Med. Biol. 38, 71–92 (1993).
[CrossRef] [PubMed]

H. H. Barrett, D. W. Wilson, B. M. W. Tsui, “Noise properties of the EM algorithm: I. Theory,” Phys. Med. Biol. 39, 833–846 (1994).
[CrossRef] [PubMed]

D. W. Wilson, B. M. W. Tsui, H. H. Barrett, “Noise properties of the EM algorithm: II. Monte Carlo simulations,” Phys. Med. Biol. 39, 847–872 (1994).
[CrossRef]

Proc. Natl. Acad. Sci. (USA) (1)

H. H. Barrett, J. Yao, J. P. Rolland, K. J. Myers, “Model observers for assessment of image quality,” Proc. Natl. Acad. Sci. (USA) 90, 9758–9765 (1993).
[CrossRef]

Proc. Symp. Appl. Math. (1)

R. A. Horn, “The Hadamard product,” Proc. Symp. Appl. Math. 40, 87–169 (1990).
[CrossRef]

Rep. Prog. Phys. (UK) (1)

R. Shaw, “Evaluating the efficiency of imaging processes,” Rep. Prog. Phys. (UK) 41, 1103–1155 (1978).
[CrossRef]

Science (2)

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

J. A. Swets, “Measuring the accuracy of diagnostic systems,” Science 240, 1285–1293 (1988);J. A. Swets, R. M. Pickett, Evaluation of Diagnostic Systems (Academic, New York, 1982).
[CrossRef] [PubMed]

Other (21)

K. M. Hanson, “Variations in task and the ideal observer,” in Application of Optical Instrumentation in Medicine XI (Atlanta), G. D. Fullerton, ed., Proc. Soc. Photo-Opt. Instrum. Eng.419, 60–67 (1983).
[CrossRef]

K. M. Hanson, “Optimization for object localization of the constrained algebraic reconstruction technique,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 146–153 (1989).
[CrossRef]

M. F. Kijewski, “The Barankin bound: a model of detection with location uncertainty,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 153–160 (1992).
[CrossRef]

R. F. Wagner, K. J. Myers, D. G. Brown, M. J. Tapiovaara, A. E. Burgess, “Higher-order tasks: human vs. machine performance,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 183–194 (1989).
[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. Soc. Photo-Opt. Instrum. Eng.314, 72–76 (1981).
[CrossRef]

J. C. Dainty, R. Shaw, Image Science (Academic, London, 1974).

J. Yao, H. H. Barrett, “Predicting human performance by a channelized Hotelling observer model,” in Mathematical Methods in Medical Imaging, D. C. Wilson, J. N. Wilson, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1768, 161–168 (1992).
[CrossRef]

J. Yao, “Predicting human performance by model observers,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1994).

A. B. Whalen, Detection of Signals in Noise (Academic, New York, 1971).

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

K. V. Mardia, J. T. Kent, J. M. Bibby, Multivariate Analysis (Academic, San Diego, Calif., 1979).

M. Siotani, T. Hayakawa, Y. Fujikoshi, Modern Multi-variate Statistical Analysis: A Graduate Course and Handbook (American Sciences, Columbus, Ohio, 1985).

H. H. Barrett, “The Radon transform and its applications,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1984), Vol. 21, pp. 219–285.
[CrossRef]

J. Pilz, Bayesian Estimation and Experimental Design in Linear Regression Models (Wiley, Bergakademie Freiberg, Germany, 1991).

A. O. Hero, J. A. Fessler, “A fast recursive algorithm for computing CR-type bounds for image reconstruction problems,” presented at the Institute of Electrical and Electronics Engineers Nuclear Science Symposium, Orlando, Fla., October 1992.

N. E Hartsough, H. H. Barrett, H. B. Barber, J. M. Woolfenden, “Predicting the performance of gamma-ray imaging devices in the task of tumor detection,” in Proceedings of the 1991 IEEE Medical Imaging Conference, Orlando, Fla. (Institute of Electrical and Electronics Engineers, New York, 1992), pp. 2113–2117).

K. J. Myers, R. F. Wagner, K. M. Hanson, H. H. Barrett, J. P. Rolland, “Human and quasi-Bayesian observers of images limited by quantum noise, object variability, and artifacts,” in Medical Imaging 1994: Image Perception, H. L. Kundel, ed., Proc. Soc. Photo-Opt. Instrum. Eng.2166, 180–190 (1994).
[CrossRef]

J. P. Rolland, “Factors influencing lesion detection in medical imaging,” Ph.D. dissertation (University of Arizona, Tucson, Arizona, 1990).

L. Rade, B. Westergren, Beta Mathematics Handbook (CRC, Boca Raton, Fla., 1989).

H. H. Barrett, J. P. Rolland, R. F. Wagner, K. J. Myers, “Detection of known signals in inhomogeneous, random backgrounds,” in Medical Imaging III: Image Formation, S. J. Dwyer, R. G. Jost, R. H. Schneider, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1090, 176–182 (1989).
[CrossRef]

R. G. Paxman, “Coordinated design of restoration algorithm and coded aperture,” Ph.D. dissertation (University of Arizona, Tucson, Ariz., 1984).

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Tables (1)

Tables Icon

Table 1 Summary of Figures of Merit

Equations (113)

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

f ( r ) = k = 1 F k Φ k ( r ) ,
Φ k ( r ) = exp ( 2 π i ρ k · r ) S ( r ) .
m = S f ( r ) h m ( r ) d r .
g = + = f ( r ) + ,
g = k = 1 F k Φ k ( r ) + = k = 1 F k Φ k ( r ) + .
g m = k = 1 F k [ Φ k ( r ) ] m + m = k = 1 Ψ m k F k + m .
Ψ m k = [ Φ k ( r ) ] m = S h m ( r ) exp ( 2 π i ρ k · r ) d r ,
g = Ψ F + ,
β k k = m = 1 M Ψ m k * Ψ m k .
B = Ψ Ψ ,
β k k = m = 1 M [ Φ k ( r ) ] m * [ Φ k ( r ) ] m = ( Φ k ( r ) , Φ k ( r ) ) ,
β k k = m = 1 M | Ψ m k | 2 = m = 1 M | S h m ( r ) exp ( 2 π i ρ k · r ) d r | 2 ,
cos θ k k = | β k k | 2 β k k β k k .
h m ( x ) = rect ( x m Δ w ) ,
Ψ m k = m Δ w / 2 m Δ + w / 2 exp ( 2 π i ξ k x ) d x = exp ( 2 π i ξ k m Δ ) w sinc ( w ξ k ) ,
β k k = ( 2 M + 1 ) w 2 sinc 2 ( w ξ k )
β k k = w 2 sinc ( w ξ k ) sinc ( w ξ k ) = sin [ ( 2 M + 1 ) a ] sin ( a ) ,
h m ( x ) = m Δ w / 2 m Δ + w / 2 d x p lens ( x x ) .
Ψ m k = L / 2 L / 2 d x m Δ w / 2 m Δ + w / 2 d x p lens ( x x ) exp ( 2 π i ξ k x ) = L / 2 L / 2 d x p tot ( x m Δ ) exp ( 2 π i ξ k x ) ,
Ψ m k P tot ( ξ k ) exp ( 2 π i ξ k m Δ ) ,
β k k P tot * ( ξ k ) P tot ( ξ k ) m = M M exp [ 2 π i ( ξ k ξ k ) m Δ ] P tot * ( ξ k ) P tot ( ξ k ) 1 Δ L / 2 L / 2 d x exp [ 2 π i ( ξ k ξ k ) x ] .
β k k L Δ | P t o t ( ξ k ) | 2 δ k k .
h m n ( r ) = 1 w rect [ p m r cos ( θ ϕ n ) w ] ,
Ψ m n k = 2 R 2 p m 2 sinc [ w ρ k cos ( ϕ n α k ) ] × sinc [ 2 R 2 p m 2 ρ k sin ( ϕ n α k ) ] × exp { 2 π i [ ρ k p m cos ( ϕ n α k ) ] } ,
β k k = m , n 4 ( R 2 p m 2 ) sinc 2 [ w ρ k cos ( ϕ n α k ) ] × sinc 2 [ 2 R 2 p m 2 ρ k sin ( ϕ n α k ) ] ,
[ J θ ] k k = θ k ln p ( g | θ ) θ k ln p ( g | θ ) = 2 θ k θ k ln p ( g | θ ) ,
var ( θ ̂ k ) [ J θ 1 ] k k .
K ̂ θ J θ 1 .
var ( θ ̂ k ) [ J θ 1 ] k k 1 [ J θ ] k k ,
J k k = 2 F k * F k ln p ( g | F ) ,
p ( g | F ) = 1 ( 2 π ) M / 2 det ( K ) × exp [ 1 2 ( g ) t K 1 ( g ) ] ,
J k k = m = 1 M m = 1 M Ψ m k * ( K 1 ) m m Ψ m k = [ Ψ K 1 Ψ ] k k .
[ K ] m m = σ m 2 δ m m ,
J k k = m = 1 M Ψ m k * Ψ m k σ m 2 .
p ( g | F ) = m = 1 M ( m ) g m g m ! exp ( m ) = m = 1 M ( Ψ F ) m g m g m ! exp [ ( Ψ F ) m ] .
J k k = m = 1 M Ψ m k * Ψ m k ( Ψ F ) m = m = 1 M Ψ m k * Ψ m k m .
[ K ] m m = ( Ψ F ) m δ m m .
var ( F ̂ k ) | F ̂ k F k | 2 ,
var ( F ̂ k ) ( J N 1 ) k k 1 J k k , k = 1 . . . N .
J k k = m = 1 M | Ψ m k | 2 m .
eff ( k ) m = 1 M | Ψ m k | 2 m / m = 1 M | Ψ m k | 2 .
m = eff ( k ) + δ m ( k ) ,
1 m = 1 eff ( k ) δ m ( k ) [ eff ( k ) ] 2 + [ δ m ( k ) ] 2 [ eff ( k ) ] 3 + . . . .
J k k = m = 1 M | Ψ m k | 2 eff ( k ) + m = 1 M | Ψ m k | 2 [ δ m ] 2 [ eff ( k ) ] 3 + . . . .
var ( F ̂ k ) eff ( k ) / β k k .
w = K 1 Δ ,
Δ = { f 2 ( r ) f 1 ( r ) } = Ψ [ F 2 F 1 ] Ψ Δ F .
[ SNR ( SKE / BKE , Hot , g ) ] 2 = Δ K 1 Δ = m = 1 M [ Δ m ] 2 σ m 2 ,
[ SNR ( SKE / BKE , Hot , g ) ] 2 = m = 1 M [ ( Ψ Δ F ) m ] 2 σ m 2 = k = 1 k = 1 Δ F k * Δ F k m = 1 M Ψ m k * Ψ m k σ m 2 = Δ F J Δ F .
[ SNR ( SKE / BKE , Hot , g ) ] 2 = 1 σ 2 k = 1 k = 1 Δ F k * Δ F k m = 1 M Ψ m k * Ψ m k = 1 σ 2 Δ F B Δ F .
[ SNR ( SKE / BKE , Hot , g ) ] 2 = 1 σ 2 k = 1 β k k | Δ F k | 2 .
[ SNR ( SKE / BKE , Hot , F ̂ ) ] 2 = Δ F ̂ ¯ K ̂ F 1 Δ F ̂ ¯ ,
[ SNR ( SKE / BKE , Hot , F ̂ ) ] 2 = Δ F J N Δ F .
S 2 g = Ψ S 2 F Ψ + K ¯ ,
[ SNR ( SKE / RBG , Hot , g ) ] 2 = [ Ψ Δ F ] [ Ψ S 2 F Ψ + K ¯ ] 1 Ψ Δ F .
S ̂ 2 F = S 2 F + J ¯ N 1 ,
[ SNR ( SKE / RBG , Hot , F ̂ ) ] 2 = Δ F [ S 2 F + J ¯ N 1 ] 1 Δ F .
[ K F ] k k [ F k F ¯ k ] * [ F k F ¯ k ] = W k δ k k ,
R f ( r , r ) [ f ( r ) f ¯ ( r ) ] [ f ( r ) f ¯ ( r ) ] = k = 1 k = 1 W k δ k k Φ k * ( r ) Φ k ( r ) = S ( r ) S ( r ) k = 1 W k exp [ 2 π i ρ k · ( r r ) ] .
[ SNR ( SKE / LBG , Hot , F ̂ ) ] 2 = Δ F [ K F + J ¯ N 1 ] 1 Δ F .
[ SNR ( SKE / LBG , Hot , F ̂ ) ] 2 = k = 1 N | Δ F ¯ k | 2 J ¯ k k 1 + W k J ¯ k k .
θ = S d r t ( r ) f ( r ) ,
t ( r ) = k = 1 N T k Φ k ( r ) .
θ ̂ = S d r t ( r ) k = 1 N F ̂ k Φ k ( r ) = S d r k = 1 N T k * Φ k * ( r ) k = 1 N F ̂ k Φ k ( r ) ,
S d r Φ k * ( r ) Φ k ( r ) = V δ k k ,
θ ̂ = k = 1 N T k * F ̂ k = T F ̂ .
θ ̂ = k = 1 N T k * F ̂ k = T F = θ ,
var ( θ ̂ ) = T J N 1 T ,
var ( θ ̂ ) = k = 1 N | T k | 2 J k k .
Ψ m k = S d r K δ ( r r 0 ) Φ k ( r ) = K exp ( 2 π i ρ k · r 0 ) .
β k k = M K 2 exp [ 2 π i ( ρ k ρ k ) · r 0 ]
J k k = K 2 exp [ 2 π i ( ρ k ρ k ) · r 0 ] m = 1 M 1 σ m 2 ,
[ SNR ( r 0 ) ] 2 = k = 1 N k = 1 N x 0 k * A k k x 0 k exp [ 2 π i ( ρ k ρ k ) · r 0 ] .
SNR 2 = 1 V S d r 0 [ SNR ( r 0 ) ] 2 = k = 1 N k = 1 N x 0 k * A k k x 0 k 1 V S d r 0 exp [ 2 π i ( ρ k ρ k ) · r 0 ] k = 1 N | x 0 k | 2 A k k ,
( K + J 1 ) 1 = [ K 1 / 2 ( I + K 1 / 2 J 1 K 1 / 2 ) K 1 / 2 ] 1 = K 1 / 2 ( I + K 1 / 2 J 1 K 1 / 2 ) 1 K 1 / 2 .
[ SNR ( SKE / RBG , Hot , F ̂ ) ] 2 k = 1 N | ( K F 1 / 2 Δ F ) k | 2 1 + [ K F 1 / 2 J ¯ N 1 K F 1 / 2 ] k k ,
[ SNR ( SKE / LBG , Hot , F ̂ ) ] 2 k = 1 N | Δ F k | 2 J ¯ k k 1 + [ K F ] k k J ¯ k k k = 1 N | Δ F k | 2 β k k eff ( k ) + [ K F ] k k β k k ,
[ SNR ( SKE / BKE , LSIV , stat ) ] 2 = d 2 ρ { [ G 0 MTF ( ρ ) ] 2 NPS ( ρ ) } | Δ F ( ρ ) | 2 ,
[ SNR ( SKE / LBG , LSIV , stat ) ] 2 = d 2 ρ { [ G 0 MTF ( ρ ) ] 2 W ( ρ ) [ G 0 MTF ( ρ ) ] 2 + NPS ( ρ ) } | Δ F ( ρ ) | 2 ,
GNEQ ( ρ ) = [ G 0 MTF ( ρ ) ] 2 W ( ρ ) [ G 0 MTF ( ρ ) ] 2 + N 0 .
var ( F ̂ k ) = ( J n 1 ) k k 1 J k k
var ( F ̂ k ) = eff ( k ) β k k
k = 1 | Δ F k | 2 β k k eff ( k )
k = 1 N | Δ F k | 2 β k k eff ( k )
Δ F [ K F + J ¯ N 1 ] 1 Δ F
k = 1 N | Δ F ¯ k | 2 β k k eff ( k ) + W k β k k
var ( θ ̂ ) = T J N 1 T
k = 1 N | T k | 2 eff ( k ) β k k
O = n = 1 N α n u n u n ,
O i i = n = 1 N α n | u n i | 2 ,
O 1 = n = 1 N 1 α n u n u n ,
[ O 1 ] i i = n = 1 N 1 α n | u n i | 2 .
n = 1 N a n 2 n = 1 N b n 2 [ n = 1 N a n b n ] 2 .
O i i [ O 1 ] i i = n = 1 N α n | u n i | 2 n = 1 N 1 α n | u n i | 2 [ n = 1 N | u n i | 2 ] 2 = 1 ,
O i i [ O 1 ] i i 1 ,
( I + O 1 ) 1 = n = 1 N λ n 1 + λ n u n u n .
[ ( I + O 1 ) 1 ] k k = n = 1 N λ n 1 + λ n | u n k | 2 .
f [ α t 1 + ( 1 α ) t 2 ] α f ( t 1 ) + ( 1 α ) f ( t 2 ) , 0 α 1 .
f ( n α n t n ) n α n f ( t n ) , n α n = 1 , α n 1.
n λ n | u n k | 2 1 + n λ n | u n k | 2 n λ n 1 + λ n | u n k | 2 .
[ ( I + O 1 ) 1 ] k k O k k 1 + O k k ,
s n ( g , F ) = F n ln p ( g | F ) .
F ̂ eff = F + J 1 s ( g , F ) ,
s ( g , F ̂ ML ) = 0 .
s ( g , F ) = Ψ K 1 ( g Ψ F ) .
J 1 = ( Ψ K 1 Ψ ) 1 ,
F ̂ eff = ( Ψ K 1 Ψ ) 1 Ψ K 1 g .
s n ( g , F ) = m = 1 M Ψ m n * [ g m ( Ψ F ) m 1 ] .
s ( g , F ) = Ψ [ g Ψ F 1 ] ,
s ( g , F ̂ ML ) = Ψ [ g Ψ F ̂ ML 1 ] = 0 .
g Ψ F ̂ ML 1 = Ψ F Ψ δ F ̂ ML Ψ F + . . . ,
Ψ [ Ψ δ F ̂ Ψ F ] = Ψ diag ( 1 Ψ F ) Ψ δ F ̂ = J δ F ̂ ,
δ F ̂ = J 1 Ψ [ Ψ F ] .

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