Advertisement

Poisson Approximation of Image Processes in Computer Tomography

  • D. Pfeifer
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

We present estimations and asymptotic expansions for the total variation distance between the superposition of independent Bernoulli point processes and the Poisson point process with the same intensity measure. Special emphasis is given to the lattice case which arises in connection with the image reconstruction in computer tomography.

Keywords

Positron Emission Tomography Asymptotic Expansion Point Process Regional Cerebral Blood Flow Poisson Point Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A.D. Barbour (1988): Stein’s method and Poisson process convergence. J. Appl. Prob. 25A (special volume): A Celebration of Applied Probability, 175–184.MathSciNetCrossRefGoogle Scholar
  2. A.D. Barbour and P. Hall (1984): On the rate of Poisson convergence. Math. Proc. Camb. Phil. Soc. 95, 473–480.zbMATHMathSciNetCrossRefGoogle Scholar
  3. P. Deheuvels and D. Pfeifer (1988): Poisson approximations of multinomial distributions and point processes. J. Multivar. Analysis 25, 65–89.zbMATHMathSciNetCrossRefGoogle Scholar
  4. R.S.J. Frackowiak, G.-L. Lenzi, T. Jones and J.D. Heather (1980): Quantitative measurement of regional cerebral blood flow and oxygen metabolism in man using 15 O and positron emission tomography: theory, procedure, and normal values. J. Computer Ass. Tomography 6, 727–736.CrossRefGoogle Scholar
  5. S. Geman and D.E. McClure (1987): Statistical methods for tomographic image reconstruction. Invited paper No. 21.1, 46th Session of the ISI. Bulletin of the International Statistical Institute, Proceedings of the 46th Session, Tokyo 1987, Vol. 4, 5–21.Google Scholar
  6. A.F. Karr (1986): Point Processes and their Statistical Inference. Marcel Dekker.Google Scholar
  7. Y.V. Prohorov (1953): Asymptotic behavior of the binomial distribution. Usp. Mat. Nauk 8, no. 3(55), 135–142.MathSciNetGoogle Scholar
  8. Y. Vardi, L.A. Shepp and L. Kaufman (1985): A statistical model for positron emission tomography. JASA 80, 8–20.zbMATHMathSciNetGoogle Scholar
  9. H.J. Witte (1988): Multivariate Poissonapproximation. Ph.D. Thesis, RWTH Aachen.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1991

Authors and Affiliations

  • D. Pfeifer
    • 1
  1. 1.Fachbereich MathematikUniversität OldenburgOldenburgGermany

Personalised recommendations