Abstract

Numerical observers are investigated for predicting the outcome of a free-response human observer study involving the detection of simulated pulmonary nodules in images reconstructed from low-dose computed tomography projection data by use of several reconstruction algorithms. A new way of calculating the figure of merit of a numerical observer is proposed wherein the detectability of signals in a particular image depends on the noise properties associated with that image and not the other images in the data set. The resulting variants of numerical observers are found to perform better than their traditional counterparts. In particular, the imagewise variant of the region-of-interest observer is found to predict best the rank ordering of algorithms by human observers for the free-response task.

© 1999 Optical Society of America

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  33. S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
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  34. P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
    [CrossRef]
  35. L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
    [CrossRef]
  36. J. Browne, A. R. De Pierro, “A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography,” IEEE Trans. Med. Imaging 15, 687–699 (1996).
    [CrossRef]
  37. K. T. D. Yeung, G. T. Herman, “Objective measures to evaluate the performance of image reconstruction algorithms,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. Jost, R. H. Schneider, eds., Proc. SPIE1092, 326–335 (1989).
    [CrossRef]
  38. 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] [PubMed]
  39. 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. SPIE1768, 161–168 (1992).
    [CrossRef]
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  41. C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.
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    [CrossRef]

1996 (2)

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

J. Browne, A. R. De Pierro, “A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography,” IEEE Trans. Med. Imaging 15, 687–699 (1996).
[CrossRef]

1994 (3)

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening observer model,” J. Opt. Soc. Am. A 11, 1237–1242 (1994).
[CrossRef]

1993 (2)

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

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] [PubMed]

1992 (2)

T. A. Gooley, H. H. Barrett, “Evaluation of statistical methods of image reconstruction through ROC analysis,” IEEE Trans. Med. Imaging 11, 276–283 (1992).
[CrossRef]

R. M. Lewitt, “Alternatives to voxels for image representation in iterative reconstruction algorithms,” Phys. Med. Biol. 37, 705–716 (1992).
[CrossRef] [PubMed]

1991 (1)

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

1990 (3)

1989 (3)

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

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–243 (1989).
[CrossRef] [PubMed]

D. P. Chakraborty, “Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data,” Med. Phys. 16, 561–568 (1989).
[CrossRef] [PubMed]

1987 (2)

1986 (2)

1985 (1)

1982 (1)

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef]

1981 (1)

P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
[CrossRef]

1979 (1)

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 4, 109–112 (1979).
[CrossRef]

1978 (1)

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

Abbey, C. K.

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal-to-noise ratios for the ML-EM algorithm,” in Medical Imaging, 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 47–58 (1996).
[CrossRef]

C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.

Barrett, H. H.

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] [PubMed]

T. A. Gooley, H. H. Barrett, “Evaluation of statistical methods of image reconstruction through ROC analysis,” IEEE Trans. Med. Imaging 11, 276–283 (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, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
[CrossRef] [PubMed]

R. D. Fiete, H. H. Barrett, W. E. Smith, K. J. Myers, “Hotelling trace criterion and its correlation with human-observer performance,” J. Opt. Soc. Am. A 4, 945–953 (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, 717–723 (1986).
[CrossRef]

K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton, D. 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]

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal-to-noise ratios for the ML-EM algorithm,” in Medical Imaging, 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 47–58 (1996).
[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. SPIE1768, 161–168 (1992).
[CrossRef]

C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.

Baxter, L. R.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Borgstrom, M. C.

Brown, D. G.

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 II, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE1090, 183–194 (1989).
[CrossRef]

Browne, J.

J. Browne, A. R. De Pierro, “A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography,” IEEE Trans. Med. Imaging 15, 687–699 (1996).
[CrossRef]

Browne, J. A.

J. A. Browne, G. T. Herman, D. Odhner, “SNARK93— a programming system for image reconstruction from projections,” (Department of Radiology, University of Pennsylvania, Philadelphia, Pa., 1993).

Bunch, P. C.

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

Burgess, A.

A. Burgess, X. Li, “Experimental evaluation of observer models for detection of signals in statistically defined backgrounds,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 89–100.

Burgess, A. E.

A. E. Burgess, “Statistically defined backgrounds: performance of a modified nonprewhitening observer model,” J. Opt. Soc. Am. A 11, 1237–1242 (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 II, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE1090, 183–194 (1989).
[CrossRef]

Chakraborty, D. P.

D. P. Chakraborty, L. H. L. Winter, “Free-response methodology: alternate analysis and a new observer-performance experiment,” Radiology 174, 873–881 (1990).
[PubMed]

D. P. Chakraborty, “Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data,” Med. Phys. 16, 561–568 (1989).
[CrossRef] [PubMed]

De Pierro, A. R.

J. Browne, A. R. De Pierro, “A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography,” IEEE Trans. Med. Imaging 15, 687–699 (1996).
[CrossRef]

de Vries, D. J.

M. A. King, D. J. de Vries, E. J. Soares, “Comparison of the channelized Hotelling and human observers for lesion detection in hepatic SPECT imaging,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 14–20 (1997).
[CrossRef]

Efron, B.

B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans (Society For Industrial and Applied Mathematics, Philadelphia, Pa., 1982).

Eggermont, P. P. B.

P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
[CrossRef]

Fiete, R. D.

Furuie, S. S.

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

Gibbons, J. D.

M. Kendall, J. D. Gibbons, Rank Correlation Methods (Oxford U. Press, New York, 1990).

Gooley, T. A.

T. A. Gooley, H. H. Barrett, “Evaluation of statistical methods of image reconstruction through ROC analysis,” IEEE Trans. Med. Imaging 11, 276–283 (1992).
[CrossRef]

Grafton, S. T.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Green, D. M.

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, Calif., 1988).

Griffeth, L. K.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Hall, T. J.

M. F. Insana, T. J. Hall, “Methods for estimating the efficiency of human and computational observers in ultrasonography,” in Information Processing in Medical Imaging, H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, Berlin, 1993), Vol. 687, pp. 542–552.

Hamilton, J. F.

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

Hanson, K. M.

Hawkins, R. A.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Herman, G. T.

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

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

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

P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
[CrossRef]

J. A. Browne, G. T. Herman, D. Odhner, “SNARK93— a programming system for image reconstruction from projections,” (Department of Radiology, University of Pennsylvania, Philadelphia, Pa., 1993).

K. T. D. Yeung, G. T. Herman, “Objective measures to evaluate the performance of image reconstruction algorithms,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. Jost, R. H. Schneider, eds., Proc. SPIE1092, 326–335 (1989).
[CrossRef]

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

G. T. Herman, “Algorithms for computed tomography,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (CRC Press, Boca Raton, Fla., 1998), Chap. 26, pp. 1–9.

Hoffman, E. J.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Hoh, C. K.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Insana, M. F.

M. F. Insana, T. J. Hall, “Methods for estimating the efficiency of human and computational observers in ultrasonography,” in Information Processing in Medical Imaging, H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, Berlin, 1993), Vol. 687, pp. 542–552.

Karp, J. S.

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

Kendall, M.

M. Kendall, J. D. Gibbons, Rank Correlation Methods (Oxford U. Press, New York, 1990).

Kinahan, P.

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

King, M. A.

M. A. King, D. J. de Vries, E. J. Soares, “Comparison of the channelized Hotelling and human observers for lesion detection in hepatic SPECT imaging,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 14–20 (1997).
[CrossRef]

Lent, A.

P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
[CrossRef]

Lewitt, R. M.

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

R. M. Lewitt, “Alternatives to voxels for image representation in iterative reconstruction algorithms,” Phys. Med. Biol. 37, 705–716 (1992).
[CrossRef] [PubMed]

Li, X.

A. Burgess, X. Li, “Experimental evaluation of observer models for detection of signals in statistically defined backgrounds,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 89–100.

Llacer, J.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Matej, S.

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

Mazziotta, J. C.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Metz, C. E.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–243 (1989).
[CrossRef] [PubMed]

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

Mould, R. F.

R. F. Mould, Introduction to Medical Statistics, 2nd ed. (Hilger, Bristol, UK, 1989).

Myers, K. J.

Narayan, T. K.

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

Odhner, D.

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

J. A. Browne, G. T. Herman, D. Odhner, “SNARK93— a programming system for image reconstruction from projections,” (Department of Radiology, University of Pennsylvania, Philadelphia, Pa., 1993).

Patton, D. D.

Pernkopf, E.

E. Pernkopf, Atlas of Topographical and Applied Human Anatomy (Saunders, Philadelphia, Pa., 1964), Vol. 2.

Pickett, R. M.

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

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] [PubMed]

Sanderson, G. K.

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

Seeley, D. W.

Shepp, L. A.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef]

Simmons, A. H.

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

Smith, W. E.

Soares, E. J.

M. A. King, D. J. de Vries, E. J. Soares, “Comparison of the channelized Hotelling and human observers for lesion detection in hepatic SPECT imaging,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 14–20 (1997).
[CrossRef]

Swensson, R. G.

R. G. Swensson, “Measuring detection and localization performance,” in Information Processing in Medical Imaging, H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, Berlin, 1993), Vol. 687, pp. 525–541.

Swets, J. A.

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 4, 109–112 (1979).
[CrossRef]

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, Calif., 1988).

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

Tapiovaara, M. J.

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 II, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE1090, 183–194 (1989).
[CrossRef]

Vardi, Y.

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef]

Veklerov, E.

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

Wagner, R. F.

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 II, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE1090, 183–194 (1989).
[CrossRef]

Wilson, D. W.

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal-to-noise ratios for the ML-EM algorithm,” in Medical Imaging, 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 47–58 (1996).
[CrossRef]

Winter, L. H. L.

D. P. Chakraborty, L. H. L. Winter, “Free-response methodology: alternate analysis and a new observer-performance experiment,” Radiology 174, 873–881 (1990).
[PubMed]

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] [PubMed]

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. SPIE1768, 161–168 (1992).
[CrossRef]

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]

K. T. D. Yeung, G. T. Herman, “Objective measures to evaluate the performance of image reconstruction algorithms,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. Jost, R. H. Schneider, eds., Proc. SPIE1092, 326–335 (1989).
[CrossRef]

IEEE Trans. Med. Imaging (5)

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

T. A. Gooley, H. H. Barrett, “Evaluation of statistical methods of image reconstruction through ROC analysis,” IEEE Trans. Med. Imaging 11, 276–283 (1992).
[CrossRef]

S. Matej, R. M. Lewitt, “Practical considerations for 3-D image reconstruction using spherically symmetric volume elements,” IEEE Trans. Med. Imaging 15, 68–78 (1996).
[CrossRef] [PubMed]

L. A. Shepp, Y. Vardi, “Maximum likelihood reconstruction in positron emission tomography,” IEEE Trans. Med. Imaging 1, 113–122 (1982).
[CrossRef]

J. Browne, A. R. De Pierro, “A row-action alternative to the EM algorithm for maximizing likelihoods in emission tomography,” IEEE Trans. Med. Imaging 15, 687–699 (1996).
[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]

Invest. Radiol. (3)

C. E. Metz, “Some practical issues of experimental design and data analysis in radiological ROC studies,” Invest. Radiol. 24, 234–243 (1989).
[CrossRef] [PubMed]

J. A. Swets, “ROC analysis applied to the evaluation of medical imaging techniques,” Invest. Radiol. 4, 109–112 (1979).
[CrossRef]

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

J. Appl. Photogr. Eng. (1)

P. C. Bunch, J. F. Hamilton, G. K. Sanderson, A. H. Simmons, “A free-response approach to the measurement and characterization of radiographic-observer performance,” J. Appl. Photogr. Eng. 4, 166–171 (1978).

J. Nucl. Med. (1)

J. Llacer, E. Veklerov, L. R. Baxter, S. T. Grafton, L. K. Griffeth, R. A. Hawkins, C. K. Hoh, J. C. Mazziotta, E. J. Hoffman, C. E. Metz, “Results of a clinical receiver operating characteristic study comparing filtered backprojection and maximum likelihood estimator images in FDG PET studies,” J. Nucl. Med. 34, 1198–1203 (1993).
[PubMed]

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

Linear Algebr. Appl. (1)

P. P. B. Eggermont, G. T. Herman, A. Lent, “Iterative algorithms for larger partitioned systems with applications to image reconstruction,” Linear Algebr. Appl. 40, 37–67 (1981).
[CrossRef]

Med. Phys. (1)

D. P. Chakraborty, “Maximum likelihood analysis of free-response receiver operating characteristic (FROC) data,” Med. Phys. 16, 561–568 (1989).
[CrossRef] [PubMed]

Phys. Med. Biol. (3)

R. M. Lewitt, “Alternatives to voxels for image representation in iterative reconstruction algorithms,” Phys. Med. Biol. 37, 705–716 (1992).
[CrossRef] [PubMed]

S. S. Furuie, G. T. Herman, T. K. Narayan, P. Kinahan, J. S. Karp, R. M. Lewitt, S. Matej, “A methodology for testing for statistically significant differences between fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 341–354 (1994).
[CrossRef] [PubMed]

S. Matej, G. T. Herman, T. K. Narayan, S. S. Furuie, R. M. Lewitt, P. Kinahan, “Evaluation of task-oriented performance of several fully 3-D PET reconstruction algorithms,” Phys. Med. Biol. 39, 355–367 (1994).
[CrossRef] [PubMed]

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] [PubMed]

Radiology (1)

D. P. Chakraborty, L. H. L. Winter, “Free-response methodology: alternate analysis and a new observer-performance experiment,” Radiology 174, 873–881 (1990).
[PubMed]

Other (19)

D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, Calif., 1988).

M. F. Insana, T. J. Hall, “Methods for estimating the efficiency of human and computational observers in ultrasonography,” in Information Processing in Medical Imaging, H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, Berlin, 1993), Vol. 687, pp. 542–552.

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

G. T. Herman, Image Reconstruction from Projections: The Fundamentals of Computerized Tomography (Academic, New York, 1980).

R. G. Swensson, “Measuring detection and localization performance,” in Information Processing in Medical Imaging, H. H. Barrett, A. F. Gmitro, eds. (Springer-Verlag, Berlin, 1993), Vol. 687, pp. 525–541.

M. Kendall, J. D. Gibbons, Rank Correlation Methods (Oxford U. Press, New York, 1990).

C. K. Abbey, H. H. Barrett, D. W. Wilson, “Observer signal-to-noise ratios for the ML-EM algorithm,” in Medical Imaging, 1996: Image Perception, H. L. Kundel, ed., Proc. SPIE2712, 47–58 (1996).
[CrossRef]

E. Pernkopf, Atlas of Topographical and Applied Human Anatomy (Saunders, Philadelphia, Pa., 1964), Vol. 2.

J. A. Browne, G. T. Herman, D. Odhner, “SNARK93— a programming system for image reconstruction from projections,” (Department of Radiology, University of Pennsylvania, Philadelphia, Pa., 1993).

G. T. Herman, “Algorithms for computed tomography,” in The Digital Signal Processing Handbook, V. K. Madisetti, D. B. Williams, eds. (CRC Press, Boca Raton, Fla., 1998), Chap. 26, pp. 1–9.

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. SPIE1768, 161–168 (1992).
[CrossRef]

A. Burgess, X. Li, “Experimental evaluation of observer models for detection of signals in statistically defined backgrounds,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 89–100.

C. K. Abbey, H. H. Barrett, “Linear iterative reconstruction algorithms: study of observer performance,” in Information Processing in Medical Imaging, Y. Bizais, C. Barillot, R. Di Paola, eds. (Kluwer Academic, Dordrecht, The Netherlands, 1995), pp. 65–76.

B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans (Society For Industrial and Applied Mathematics, Philadelphia, Pa., 1982).

R. F. Mould, Introduction to Medical Statistics, 2nd ed. (Hilger, Bristol, UK, 1989).

M. A. King, D. J. de Vries, E. J. Soares, “Comparison of the channelized Hotelling and human observers for lesion detection in hepatic SPECT imaging,” in Medical Imaging 1997: Image Perception, H. L. Kundel, ed., Proc. SPIE3036, 14–20 (1997).
[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 II, R. H. Schneider, S. J. Dwyer, eds., Proc. SPIE1090, 183–194 (1989).
[CrossRef]

Medical Imaging—The Assessment of Image Quality, (International Commission on Radiation Units and Measurement, Bethesda, Md., 1996).

K. T. D. Yeung, G. T. Herman, “Objective measures to evaluate the performance of image reconstruction algorithms,” in Medical Imaging III: Image Processing, S. J. Dwyer, R. Jost, R. H. Schneider, eds., Proc. SPIE1092, 326–335 (1989).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

(a) Anatomical cross section of the human thorax (copied from Fig. 133 of Pernkopf29). (b) 255×255 digitization of a mathematically described image derived from the anatomical cross section shown in (a).

Fig. 2
Fig. 2

(a) Fig. 1(b) with the circular regions (each containing a target and its background) marked. (b) Randomly generated 255×255 phantom of the thorax, obtained from Fig. 1(b). (Note: The original gray levels have been modified to make the targets and the backgrounds easily visible.)

Fig. 3
Fig. 3

Results of the human observer study. The bar chart shows the A1 values and the associated standard deviations for the 7 observers and the 11 algorithms.

Fig. 4
Fig. 4

Performance of the 11 algorithms with the noduleness observer. The FOM is plotted as a function of the free parameter γ of the observer.

Fig. 5
Fig. 5

Modified rank orderings (taking into account the relative separation of the FOM values) of the 11 reconstruction algorithms by the different observers. The observers listed along the abscissa are (1) human observer results, (2) imagewise ROI, (3) optimum imagewise noduleness, (4) optimum noduleness, (5) imagewise max of ROI, (6) SNR, (7) contrast, (8) imagewise DOG, (9) DOG, (10) ROI, and (11) human observer results. Observe that the numerical observer rankings on the left are more similar to the human observer rankings than are the numerical observer rankings on the right.

Fig. 6
Fig. 6

Similarity measure, made with the Kendall τ coefficient, between the human observer results (with the AFROC analysis) and the following numerical observers: imagewise ROI, imagewise noduleness, noduleness, imagewise max of ROI, imagewise DOG, DOG, and ROI (as a function of the free parameter γ of the noduleness observers). The contrast observer is γ=0.0, and the SNR observer is γ=0.5. (Note that the similarity measures for the imagewise DOG and the ROI observers are identical. See column 1 of Table 1.)

Tables (1)

Tables Icon

Table 1 Rank-Ordering Similarity Measures Obtained with the Generalized Kendall τ Coefficient for α=0.0, 0.2, 0.5 between the Human Observer Results and Various Numerical Observersa

Equations (24)

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

αROI(b)=wbvb|wb|,
E[α(b)|2]-E[α(b)|1]{P2 var[α(b)|2]+P1 var[α(b)|1]}1/2,
E[α(b)|2]=1i=1Isii=1IbSiα(b),
E[α(b)|1]=1i=1Inii=1IbNiα(b),
var[α(b)|2]=1i=1Isii=1IbSi{α(b)-E[α(b)|2]}2,
var[α(b)|1]=1i=1Inii=1IbNi{α(b)-E[α(b)|1]}2,
P2=i=1Isii=1Isi+i=1Ini,
P1=i=1Inii=1Isi+i=1Ini.
SDIbi=α(b)-Ei[α(b)|1]{vari[α(b)|1]}1/2,
Ei[α(b)|1]=1nibNiα(b),
vari[α(b)|1]=1nibNi{α(b)-Ei[α(b)|1]}2.
1i=1Isii=1IbSiSDIbi.
αmax(b)=maxwWwvb|w|.
αHotchan(b)=(Uvb|2-Uvb|1)tS2-1Uvb,
S2=k=12Pk(Ub-Uvb|k)(Ub-Uvb|k)tk
Um=N(0, σm)-N(0, σm-1).
σm=12πβmμ,
αγ(b)=(m-m_)[(nv+n_v_)/(n+n_)]γ,
d=1D(βd-δd)
d=1D(βd-δd)2.
z=d=1D(βd-δd)d=1D(βd-δd)21/2
11-F-FminFmax-Fmin×10.
pj=1|CjM|kCjMxk,
cj=0.051-pj|CjM|300otherwise,

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