Abstract

A model for data acquired with the use of a charge-coupled-device camera is given and is then used for developing a new iterative method for restoring intensities of objects observed with such a camera. The model includes the effects of point spread, photoconversion noise, readout noise, nonuniform flat-field response, nonuniform spectral response, and extraneous charge carriers resulting from bias, dark current, and both internal and external background radiation. An iterative algorithm is identified that produces a sequence of estimates converging toward a constrained maximum-likelihood estimate of the intensity distribution of an imaged object. An example is given for restoring images from data acquired with the use of the Hubble Space Telescope.

© 1993 Optical Society of America

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  1. R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
    [CrossRef] [PubMed]
  2. Y. Hiraoka, J. W. Sedat, D. A. Agard, “The use of charge-coupled devices for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
    [CrossRef] [PubMed]
  3. J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).
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    [CrossRef]
  5. R. Griffiths, Hubble Space Telescope: Wide Field and Planetary Camera Instrument Handbook, Version 2.1 (Space Telescope Science Institute, Baltimore, Md., 1990).
  6. J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).
  7. H. Stark, Image Recovery, Theory and Application (Academic, New York, 1987).
  8. D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
    [CrossRef]
  9. W. H. Richardson, “Bayesian-based iterative method of image restoration,”J. Opt. Soc. Am. 62, 55–59 (1972).
    [CrossRef]
  10. L. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
    [CrossRef]
  11. L. A. Shepp, Y. Vardi, “Maximum-likelihood reconstruction for emission tomography,”IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
    [CrossRef]
  12. A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).
  13. Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
    [CrossRef]
  14. C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Stat. 11, 95–103 (1983).
    [CrossRef]
  15. H. L. Van Trees, Detection, Estimation, and Modulation Theory: Part 1 (Wiley, New York, 1968).
  16. D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer-Verlag, New York, 1991).
  17. D. G. Politte, D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,”IEEE Trans. Med. Imaging 10, 82–89 (1991).
    [CrossRef] [PubMed]
  18. W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968).
  19. D. Snyder, “Modifications of the Lucy–Richardson iteration for restoring Hubble Space-Telescopeimagery,” in The Restoration of HST Images and Spectra, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 56–61.
  20. J. Llacer, J. Nunez, “Iterative maximum-likelihood and Bayesian algorithms for image reconstruction in astronomy,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 62–69.
  21. J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
    [CrossRef]
  22. Ref. 5, p. 8.
  23. A. Tikhonov, V. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, D.C., 1977).
  24. R. Tapia, J. Thompson, Nonparametric Probability Density Estimation (The Johns Hopkins U. Press, Baltimore, Md., 1978).
  25. D. L. Snyder, M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,”IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
    [CrossRef]
  26. D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
    [CrossRef]
  27. D. G. Politte, D. L. Snyder, “The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography,”IEEE Trans. Nucl. Sci. 35, 608–610 (1988).
    [CrossRef]
  28. F. D. Murtagh, H. M. Adorf, “Detecting cosmic ray hits on HST WF/PC images using neural networks and other discriminant analysis approaches,” in Proceedings of the Fourth International Workshop on Data Analysis in Astronomy, V. Di Gesù, L. Scarsi, R. Buccheri, P. Crane, M. C. Maccarone, H. V. Zimmerman, eds. (Plenum, New York, 1992), pp. 103–111.
  29. E. J. Groth, “An algorithm for removing cosmic rays from two or more cosmic ray split exposures,” in Wide Field/Planetary Camera Final Orbital/Science Verification Report, S. M. Faber, ed. (Space Science Telescope Institute, Baltimore, Md., 1992), pp. 14–29.
  30. L. Lucy, “Restoration with increased sampling—images and spectra,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 80–87.
  31. R. L. White, C. J. Burrows, “The HST spherical aberration and its effects on images,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 2–6.

1992

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[CrossRef]

1991

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

D. G. Politte, D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,”IEEE Trans. Med. Imaging 10, 82–89 (1991).
[CrossRef] [PubMed]

1990

1989

R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
[CrossRef] [PubMed]

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

1988

D. G. Politte, D. L. Snyder, “The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography,”IEEE Trans. Nucl. Sci. 35, 608–610 (1988).
[CrossRef]

1987

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

Y. Hiraoka, J. W. Sedat, D. A. Agard, “The use of charge-coupled devices for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

1985

D. L. Snyder, M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,”IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
[CrossRef]

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

1983

C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Stat. 11, 95–103 (1983).
[CrossRef]

1982

L. A. Shepp, Y. Vardi, “Maximum-likelihood reconstruction for emission tomography,”IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

1977

A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).

1974

L. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

1972

Adorf, H. M.

F. D. Murtagh, H. M. Adorf, “Detecting cosmic ray hits on HST WF/PC images using neural networks and other discriminant analysis approaches,” in Proceedings of the Fourth International Workshop on Data Analysis in Astronomy, V. Di Gesù, L. Scarsi, R. Buccheri, P. Crane, M. C. Maccarone, H. V. Zimmerman, eds. (Plenum, New York, 1992), pp. 103–111.

Agard, D. A.

R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, D. A. Agard, “The use of charge-coupled devices for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

Aikens, R.

R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
[CrossRef] [PubMed]

Arsenin, V.

A. Tikhonov, V. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, D.C., 1977).

Blouke, M. M.

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

Burrows, C. J.

R. L. White, C. J. Burrows, “The HST spherical aberration and its effects on images,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 2–6.

Collins, S.

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

Dempster, A. D.

A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).

Elliott, T.

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

Emrick, A.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Ewing, W. S.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Feller, W.

W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1968).

Freeman, J.

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

Griffiths, R.

R. Griffiths, Hubble Space Telescope: Wide Field and Planetary Camera Instrument Handbook, Version 2.1 (Space Telescope Science Institute, Baltimore, Md., 1990).

Groth, E. J.

E. J. Groth, “An algorithm for removing cosmic rays from two or more cosmic ray split exposures,” in Wide Field/Planetary Camera Final Orbital/Science Verification Report, S. M. Faber, ed. (Space Science Telescope Institute, Baltimore, Md., 1992), pp. 14–29.

Hiraoka, Y.

Y. Hiraoka, J. W. Sedat, D. A. Agard, “The use of charge-coupled devices for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

Janesick, J. R.

J. R. Janesick, T. Elliott, S. Collins, M. M. Blouke, J. Freeman, “Scientific charge-coupled devices,” Opt. Eng. 26, 692–714 (1987).

Kaufman, L.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

Laird, N. M.

A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).

Llacer, J.

J. Llacer, J. Nunez, “Iterative maximum-likelihood and Bayesian algorithms for image reconstruction in astronomy,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 62–69.

Lucy, L.

L. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

L. Lucy, “Restoration with increased sampling—images and spectra,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 80–87.

Maniloff, J.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Miller, M. I.

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

D. L. Snyder, M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,”IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
[CrossRef]

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer-Verlag, New York, 1991).

Monteleone, D. C.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Mooney, J. M.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Murguia, J. E.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Murtagh, F. D.

F. D. Murtagh, H. M. Adorf, “Detecting cosmic ray hits on HST WF/PC images using neural networks and other discriminant analysis approaches,” in Proceedings of the Fourth International Workshop on Data Analysis in Astronomy, V. Di Gesù, L. Scarsi, R. Buccheri, P. Crane, M. C. Maccarone, H. V. Zimmerman, eds. (Plenum, New York, 1992), pp. 103–111.

Nunez, J.

J. Llacer, J. Nunez, “Iterative maximum-likelihood and Bayesian algorithms for image reconstruction in astronomy,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 62–69.

O’Sullivan, J. A.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[CrossRef]

Poddar, S. K.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Politte, D. G.

D. G. Politte, D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,”IEEE Trans. Med. Imaging 10, 82–89 (1991).
[CrossRef] [PubMed]

D. G. Politte, D. L. Snyder, “The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography,”IEEE Trans. Nucl. Sci. 35, 608–610 (1988).
[CrossRef]

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

Ribeiro, E. A.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Richardson, W. H.

Rubin, D. B.

A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).

Schulz, T. J.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[CrossRef]

Sedat, J. W.

R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
[CrossRef] [PubMed]

Y. Hiraoka, J. W. Sedat, D. A. Agard, “The use of charge-coupled devices for quantitative optical microscopy of biological structures,” Science 238, 36–41 (1987).
[CrossRef] [PubMed]

Serwer, P.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Shepherd, F. D.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Shepp, L. A.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum-likelihood reconstruction for emission tomography,”IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

Silverman, J.

J. M. Mooney, F. D. Shepherd, W. S. Ewing, J. E. Murguia, J. Silverman, “Responsivity nonuniformity limited performance of infrared staring cameras,” Opt. Eng. 28, 1151–1161 (1989).
[CrossRef]

Snyder, D.

D. Snyder, “Modifications of the Lucy–Richardson iteration for restoring Hubble Space-Telescopeimagery,” in The Restoration of HST Images and Spectra, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 56–61.

Snyder, D. L.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[CrossRef]

D. G. Politte, D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,”IEEE Trans. Med. Imaging 10, 82–89 (1991).
[CrossRef] [PubMed]

D. G. Politte, D. L. Snyder, “The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography,”IEEE Trans. Nucl. Sci. 35, 608–610 (1988).
[CrossRef]

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

D. L. Snyder, M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,”IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
[CrossRef]

D. L. Snyder, M. I. Miller, Random Point Processes in Time and Space (Springer-Verlag, New York, 1991).

Son, M.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Stark, H.

H. Stark, Image Recovery, Theory and Application (Academic, New York, 1987).

Sutherland, B. M.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Sutherland, J. C.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Tapia, R.

R. Tapia, J. Thompson, Nonparametric Probability Density Estimation (The Johns Hopkins U. Press, Baltimore, Md., 1978).

Thomas, L. J.

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

Thompson, J.

R. Tapia, J. Thompson, Nonparametric Probability Density Estimation (The Johns Hopkins U. Press, Baltimore, Md., 1978).

Tikhonov, A.

A. Tikhonov, V. Arsenin, Solutions of Ill-Posed Problems (Winston, Washington, D.C., 1977).

Trunk, J.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

Tyson, J. A.

Van Trees, H. L.

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

Vardi, Y.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

L. A. Shepp, Y. Vardi, “Maximum-likelihood reconstruction for emission tomography,”IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

White, R. L.

R. L. White, C. J. Burrows, “The HST spherical aberration and its effects on images,” in Restoration of Hubble Space Telescope Images, R. L. White, R. J. Allen, eds. (Space Telescope Science Institute, Baltimore, Md., 1990), pp. 2–6.

Wu, C. F. J.

C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Stat. 11, 95–103 (1983).
[CrossRef]

Ann. Stat.

C. F. J. Wu, “On the convergence properties of the EM algorithm,” Ann. Stat. 11, 95–103 (1983).
[CrossRef]

Astron. J.

L. Lucy, “An iterative technique for the rectification of observed distributions,” Astron. J. 79, 745–754 (1974).
[CrossRef]

Biotech.

J. C. Sutherland, B. M. Sutherland, A. Emrick, D. C. Monteleone, E. A. Ribeiro, J. Trunk, M. Son, P. Serwer, S. K. Poddar, J. Maniloff, “Quantitative electronic imaging of gel fluorescence with CCD cameras: applications to molecular biology,” Biotech. 10, 492–497 (1991).

IEEE Trans. Med. Imaging

L. A. Shepp, Y. Vardi, “Maximum-likelihood reconstruction for emission tomography,”IEEE Trans. Med. Imaging MI-1, 113–121 (1982).
[CrossRef]

D. G. Politte, D. L. Snyder, “Corrections for accidental coincidences and attenuation in maximum-likelihood image reconstruction for positron-emission tomography,”IEEE Trans. Med. Imaging 10, 82–89 (1991).
[CrossRef] [PubMed]

D. L. Snyder, M. I. Miller, L. J. Thomas, D. G. Politte, “Noise and edge artifacts in maximum-likelihood reconstructions for emission tomography,”IEEE Trans. Med. Imaging MI-6, 228–238 (1987).
[CrossRef]

IEEE Trans. Nucl. Sci.

D. G. Politte, D. L. Snyder, “The use of constraints to eliminate artifacts in maximum-likelihood image estimation for emission tomography,”IEEE Trans. Nucl. Sci. 35, 608–610 (1988).
[CrossRef]

D. L. Snyder, M. I. Miller, “The use of sieves to stabilize images produced with the EM algorithm for emission tomography,”IEEE Trans. Nucl. Sci. NS-32, 3864–3872 (1985).
[CrossRef]

IEEE Trans. Signal Process.

D. L. Snyder, T. J. Schulz, J. A. O’Sullivan, “Deblurring subject to nonnegativity constraints,”IEEE Trans. Signal Process. 40, 1143–1150 (1992).
[CrossRef]

J. Am. Stat. Assoc.

Y. Vardi, L. A. Shepp, L. Kaufman, “A statistical model for positron emission tomography,”J. Am. Stat. Assoc. 80, 8–35 (1985).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. R. Stat. Soc. B

A. D. Dempster, N. M. Laird, D. B. Rubin, “Maximum likelihood from incomplete data via the EM algorithm,”J. R. Stat. Soc. B 39, 1–38 (1977).

Methods Cell Biol.

R. Aikens, D. A. Agard, J. W. Sedat, “Solid-state imagers for microscopy,” Methods Cell Biol. 29, 291–313 (1989).
[CrossRef] [PubMed]

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