Hostname: page-component-848d4c4894-xfwgj Total loading time: 0 Render date: 2024-06-25T04:50:17.420Z Has data issue: false hasContentIssue false

An ergodic L2-theorem for simulated annealing in bayesian image reconstruction

Published online by Cambridge University Press:  14 July 2016

Gerhard Winkler*
Affiliation:
Universität München
*
Postal address: Mathematisches Institut der Ludwig-Maximillians-Universität Munchen, Theresienstrasse 39, D-8000 München 2, West Germany.

Abstract

An ergodic L2-theorem for inhomogeneous Markov chains covering simulated annealing with or without constraints and stochastic relaxation with or without constraints arising in Bayesian image reconstruction is proved. The derivation is self-contained.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1990 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Dobrushin, R. L. (1956) Central limit theorem for non-stationary Markov chains I, II. Theory Prob. Appl. 1, 6580, Theory Prob. Appl. 1, 329–383.Google Scholar
[2] Föllmer, H. (1987) Random fields and diffusion processes. In Ecole d'Été de Probabilités de Saint-Flour, XV–XVII, 1985–87, Lecture Notes in Mathematics 1362, Springer-Verlag, Berlin, pp. 101204.Google Scholar
[3] Gantert, N. (1989) Laws of large numbers for the annealing algorithm. Preprint, Universität Bonn.Google Scholar
[4] Geman, D. and Geman, S. (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell. 6, 721741.Google Scholar
[5] Geman, D. and Geman, S. (1987) Relaxation and annealing with constraints. Complex Systems Technical Report No. 35, Division of Applied Mathematics, Brown University.Google Scholar
[6] Geman, D., Geman, S., Graffigne, Chr. and Dong, Ping (1988) Boundary detection by constrained optimization. Submitted to IEEE-PAMI.Google Scholar
[7] Geman, S. and Graffigne, Chr. (1987) Markov random field models and their applications to computer vision. In Proc. 46th Session Internat. Statist. Inst. Bull. ISI 52.Google Scholar
[8] Gidas, B. (1985) Nonstationary Markov chains and convergence of the annealing algorithm. J. Statist. Phys. 39, 73131.Google Scholar
[9] Iosifescu, D. L. and Theodorescu, R. (1969) Random Processes and Learning. Grundlehren der math. Wissenschaften, Bd. 150, Springer-Verlag, New York.CrossRefGoogle Scholar