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Abstract

The point processes we consider in this chapter are useful as models for measured data acquired about an underlying, unobservable point-process when the measurements are imperfect and in the form of a point process. Such a measurement is illustrated in Fig. 3.1. Point of the underlying process, called the input point-process, occur on a space X.

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References

  1. E. S. Chornoboy, C. J. Chen, M. I. Miller, T. R. Miller, and D. L. Snyder, “An Evaluation of Maximum-Likelihood Reconstruction for SPECT,” IEEE Transactions on Medical Imaging, Vol.NS-38, 1989.

    Google Scholar 

  2. J. C. Dainty and A. H. Greenaway, “Estimation of Spatial Power Spectra in Speckle Interferometry,” J. Optical Society of America, Vol. 69, pp. 786–790, May 1979.

    Article  Google Scholar 

  3. L. C. de Freitas and J. C. Dainty, “Object Reconstruction from Photon-Limited Centroided Data of Randomly Translating Images,” Optics Letters, Vol. 13,pp. 264–266, April 1988.

    Article  Google Scholar 

  4. A.P. Dempster, N.M. Laird, and D.B. Rubin, “Maximum Likelihood from Incomplete Data via the EM Algorithm”, J. R. Statistical Society B, Vol. 39, pp. 1–37, 1977.

    MathSciNet  MATH  Google Scholar 

  5. R. D. Evans, The Atomic Nucleus, McGraw-Hill, New York, 1955.

    MATH  Google Scholar 

  6. J. R. Fienup, “Reconstruction of an Object from the Modulus of Its Fourier Transform,” Optics Letters, pp. 27–29, 1978.

    Google Scholar 

  7. J. R. Fienup, “Phase Retrieval Algorithms: A Comparison,” Applied Optics, Vol. 21,pp. 2758–2769, August 1982.

    Article  Google Scholar 

  8. I. J. Good and R. A. Gaskins, “Nonparametric Roughness Penalties for Probability Densities,” Biometrica, Vol. 58, pp.255–277, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  9. U. Grenander, Abstract Inference, Wiley, New York, 1981.

    MATH  Google Scholar 

  10. N. Hetterich and G. Weigelt, “Speckle Interferometry Observations of Pluto’s Moon Cheron,” Astronomy and Astrophysics, Vol. 125, pp. 246–248, 1983.

    Google Scholar 

  11. T. J. Holmes, D. C. Ficke, and D. L. Snyder, “Modeling of Accidental Coincidences in Both Conventional and Time-of-Flight Positron-Emission Tomography,” IEEE Transactions on Nuclear Science, Vol. NS-31, pp. 627–631, February 1984.

    Article  Google Scholar 

  12. L. S. Joyce and W. L. Root, “Precision Bounds in Super resolution Processing,” Journal of the Optical Society of America, Vol. 1, pp. 149–168, February 1984.

    Article  MathSciNet  Google Scholar 

  13. S. Kullback, Information Theory and Statistics, Wiley, New York, 1968.

    Google Scholar 

  14. K. Lange and R. Carson, “EM Reconstruction Algorithms for Emission and Transmission Tomography,” Journal of Computer Assisted Tomography, Vol. 8, pp. 306–316, April 1984.

    Google Scholar 

  15. S. A. Larsson, Gamma Emission Tomography, Acta Radiologica, Supplementum 363, ISSN 0365–5954, P. O. Box 7449, S-103 91, Stockholm, Sweden, 1980.

    Google Scholar 

  16. D. Luenberger, Optimization by Vector Space Techniques, Wiley, New York, 1969.

    Google Scholar 

  17. M.I. Miller, K.B. Larson, J. E. Saffitz, D.L. Snyder, and L.J. Thomas, Jr., “Maximum-Likelihood Estimation Applied to Electron-Microscopic Autoradiography,” J. Electron Microscope Technique, Vol. 2, pp. 611–636, 1985.

    Article  Google Scholar 

  18. M.I. Miller, B. Roysam, J. E. Saffitz, K.B. Larson, D. Fuhrmann, and L. J. Thomas, Jr., “A New Method for the Analysis of electron Microscopic Autoradiographs,” BioTechniques, Vol. 5, No.4, pp. 322–328, 1987.

    Article  Google Scholar 

  19. M. I. Miller, D. L. Snyder, and T. R. Miller, “Maximum-Likelihood Reconstruction for Single-Photon Emission Computed Tomography,” IEEE Transactions on Nuclear Science, Vol. NS-32, pp.769–778, February 1985.

    Article  Google Scholar 

  20. M.I. Miller and B. Roysam, “Bayesian Image Reconstruction for Emission Tomography - Incorporating Good’s Roughness Prior on Massively Parallel Processors,” Proc. National Academy of Sciences, April 1991.

    Google Scholar 

  21. M.J. Northcott, G. R. Ayers, and J. C. Dainty, “Algorithms for Image Reconstruction from Photon-Limited Data Using Triple Correlation,” J. Optical Soc. of Amer. A, Vol. 5, pp. 986–992, July 1988.

    Article  Google Scholar 

  22. B. Roysam, J. A. Shrauner, and M. I. Miller, “Bayesian Imaging Using Good’s Roughness Measure - Implementation on a Massively Parallel Processor,” IEEE ICASSP-88, Vol. M4.21, pp.932–935, March 1988.

    Google Scholar 

  23. T. J. Schulz, “Image Recovery for Randomly Moving Objects,” D.Sc. Thesis, Department of Electrical Engineering, Washington University, St. Louis, MO,May1990.

    Google Scholar 

  24. T. J. Schulz and D. L. Snyder, “Imaging a Randomly Moving Object from Quantum Limited Data: Applications to Image Recovery from Second and Third Order Autocorrelation,” J. Optical Society of America A, Vol. 8, pp. 801–807, May 1991.

    Article  Google Scholar 

  25. L. A. Shepp and Y. Vardi, “Maximum Likelihood Reconstruction for Emission Tomography,” IEEE Trans. on Medical Imaging, Vol. MI-1, pp. 113–121, October 1982.

    Article  Google Scholar 

  26. D.L. Snyder, L.J. Thomas, Jr.,and M.M.Ter-Pogossian, “A Mathematical Model for Positron-Emission Tomography Systems Having Time-of-Flight Measurements,” IEEE Transactions on Nuclear Science, Vol. NS-28, No.3, pp.3575–3583, 1981.

    Article  Google Scholar 

  27. D.L. Snyder, “Utilizing Side Information in Emission Tomography,” IEEE Transactions on Nuclear Science, Vol. NS-31, No.1, pp.533–537, February 1984.

    Article  Google Scholar 

  28. D. L. Snyder, M. I. Miller, L. J. Thomas,Jr., and D. G. Politte, “Noise and Edge Artifacts in Maximum-Likelihood Reconstructions for Emission Tomography,” IEEE Transactions on Medical Imaging, Vol. MI-6, pp. 228–238, September 1987.

    Article  Google Scholar 

  29. D. L. Snyder and M.I. Miller, “The Use of Sieves to Stabilize Images Produced with the EM Algorithm,” IEEE Transactions on Nuclear Science, Vol. NS-32, pp. 3864–3872, October 1985.

    Article  Google Scholar 

  30. R. A. Tapia and J. R. Thompson, Nonparametric Probability Density Estimation, Johns Hopkins University Press, Baltimore, MD,1978.

    MATH  Google Scholar 

  31. M. M. Ter-Pogossian, D. C. Ficke, M. Yamamoto, and J. T. Hood, Sr., “Super PETT I: A Positron Emission Tomograph Utilizing Photon Time-of-Flight Information,” IEEE Transactions on Medical Imaging, Vol. MI-1, pp. 179–187, 1982.

    Article  Google Scholar 

  32. A. Tikhonov, Solutions to Ill-Posed Problems, Winston and Sons, N.Y., 1977.

    Google Scholar 

  33. Y. Vardi, L. A. Shepp, and L. Kaufman, “A Statistical Model for Positron Emission Tomography,” J. American Statistical Association, Vol. 80, pp. 8–35, March 1985.

    Article  MathSciNet  MATH  Google Scholar 

  34. C. F. J. Wu, “On the Convergence Properties of the EM Algorithm,” The Annals of Statistics, Vol. 11, pp. 95–103, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  35. A. W. McCarthy, R.C. Barrett, and M.I. Miller, “Systolic Implementation of the EM Algorithm for Emission Tomography on a Mesh Connected Processor,” Proc. of the 22nd Annual Conference on Information Sciences, pp. 373–374, Princeton Univ., Princeton NJ,1988.

    Google Scholar 

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© 1991 Springer-Verlag New York, Inc.

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Snyder, D.L., Miller, M.I. (1991). Translated Poisson-Processes. In: Random Point Processes in Time and Space. Springer Texts in Electrical Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3166-0_3

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  • DOI: https://doi.org/10.1007/978-1-4612-3166-0_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7821-4

  • Online ISBN: 978-1-4612-3166-0

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