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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
S. F. Gull and J. Skilling, “Maximum entropy method in image processing,” IEE Proc, 131 F, pp. 646–659, 1984.
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.
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.
J. Skilling, “Quantified maximum entropy,” in Maximum Entropy and Bayesian Methods, P. F. Fougère, éd., pp. 341–350, Kluwer Academic, Dordrecht, 1990.
R. Bryan, “Maximum entropy analysis of oversampled data problems,” Eur. Biophys. J., 18, pp. 165–174, 1990.
W. von der Linden, R. Fischer, and V. Dose, “Evidence integrals,” In these proceedings, 1995.
J. Skilling and S. Sibisi, “Prior distributions on measure space,” In these proceedings, 1995.
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.
R. Puetter, “Pixon-based image reconstruction in high energy astrophysics,” In these proceedings, 1995.
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.
R. Fischer, Th. Fauster and W. Steinmann, “Threedimensional localization of electrons on Ag islands,” Phys. Rev. B, 48, pp. 15496–15499, 1993.
R. Fischer, “submitted to Surf. Sci.”
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Fischer, R., Von Der Linden, W., Dose, V. (1996). On the Importance of α Marginalization in Maximum Entropy. In: Hanson, K.M., Silver, R.N. (eds) Maximum Entropy and Bayesian Methods. Fundamental Theories of Physics, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5430-7_27
Download citation
DOI: https://doi.org/10.1007/978-94-011-5430-7_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6284-8
Online ISBN: 978-94-011-5430-7
eBook Packages: Springer Book Archive