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On the Importance of α Marginalization in Maximum Entropy

  • R. Fischer
  • W. Von Der Linden
  • V. Dose
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 79)

Abstract

The correct entropic prior, computed by marginalization over the reg- ularization parameter a, is used to invert photoemission data and to restore the famous “Susie” image. Comparison with the conventional maximum entropy procedure shows less overfitting of noise and demonstrates the residual ringing which is intrinsic to ill-posed inversion problems. An improvement to the steepest descent approximation reveals the reason for the overfitting. On top of that, the correct treatment of the regularization parameter is vital for the existence of the continuum-limit of MaxEnt.

Key words

Inverse Problem Regularization Entropic Prior Image Processing 

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References

  1. 1.
    S. F. Gull and J. Skilling, “Maximum entropy method in image processing,” IEE Proc, 131 F, pp. 646–659, 1984.Google Scholar
  2. 2.
    C. E. M. Strauss, D. H. Wolpert and D. R. Wolf, “Alpha, evidence, and the entropic prior,” in Maximum Entropy and Bayesian Methods (1993), G. Heidbreder, ed., Kluwer Academic, Dordrecht, 1995.Google Scholar
  3. 3.
    S. F. Gull, “Developments in maximum entropy data analysis,” in Maximum Entropy and Bayesian Methods, J. Skilling, ed., pp. 53–71, Kluwer Academic, Dordrecht, 1989.Google Scholar
  4. 4.
    J. Skilling, “Quantified maximum entropy,” in Maximum Entropy and Bayesian Methods, P. F. Fougère, éd., pp. 341–350, Kluwer Academic, Dordrecht, 1990.CrossRefGoogle Scholar
  5. 5.
    R. Bryan, “Maximum entropy analysis of oversampled data problems,” Eur. Biophys. J., 18, pp. 165–174, 1990.MathSciNetCrossRefGoogle Scholar
  6. 6.
    W. von der Linden, R. Fischer, and V. Dose, “Evidence integrals,” In these proceedings, 1995.Google Scholar
  7. 7.
    J. Skilling and S. Sibisi, “Prior distributions on measure space,” In these proceedings, 1995.Google Scholar
  8. 8.
    J. Skilling, “Fundamentals of MaxEnt in data analysis,” in Maximum Entropy in Action, B. Buck and V. A. Macaulay, eds., pp. 19–40, Clarendon Press, Oxford, 1991.Google Scholar
  9. 9.
    R. Puetter, “Pixon-based image reconstruction in high energy astrophysics,” In these proceedings, 1995.Google Scholar
  10. 10.
    R. Fischer, S. Schuppler, N. Fischer, Th. Fauster and W. Steinmann, “Image states and local work function for Ag/Pd(lll),” Phys. Rev. Lett., 70, pp. 654–657, 1993.CrossRefGoogle Scholar
  11. 11.
    R. Fischer, Th. Fauster and W. Steinmann, “Threedimensional localization of electrons on Ag islands,” Phys. Rev. B, 48, pp. 15496–15499, 1993.CrossRefGoogle Scholar
  12. 12.
    R. Fischer, “submitted to Surf. Sci.”Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1996

Authors and Affiliations

  • R. Fischer
    • 1
  • W. Von Der Linden
    • 1
  • V. Dose
    • 1
  1. 1.Max-Planck-Institut für PlasmaphysikEURATOM AssociationGarchingGermany

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