Stochastic cellular automata with Gibbsian invariant measures

A geometric characterization is given of a class of stochastic cellular automata, whose invariant probability measures are Gibbsian distributions (i.e. Markovian random fields). This class, whose members may be considered as the Cartesian product of convex polytopes with a finite number of vertices....

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Bibliographic Details
Published inIEEE transactions on information theory Vol. 37; no. 3; pp. 541 - 551
Main Authors Marroquin, J.L., Ramirez, A.
Format Journal Article
LanguageEnglish
Published New York, NY IEEE 01.05.1991
Institute of Electrical and Electronics Engineers
Subjects
Automata
Automatic programming
Bayesian methods
Computational modeling
Exact sciences and technology
Image restoration
Lattices
Markov random fields
Mathematical methods in physics
Physics
Probability distribution
Probability theory, stochastic processes, and statistics
Stochastic processes
Stochastic systems
Bayes estimation
Random field
Stochastic model
Cellular automaton
Invariant measure
Image restoration
Dynamical system
Markov field
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Summary:A geometric characterization is given of a class of stochastic cellular automata, whose invariant probability measures are Gibbsian distributions (i.e. Markovian random fields). This class, whose members may be considered as the Cartesian product of convex polytopes with a finite number of vertices. contains all known automata of this type (e.g., the Metropolis, Gibbs sampler, and heat bath algorithms), and also a new family, which is characterized by having nonreversible dynamic behavior. The fact that there is a complete geometric structure, instead of isolated points, opens the possibility of using classical techniques (such as convex programming) for the design of optimal automata. Some examples of applications are given, oriented towards the solution of image restoration problems.< >
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0018-9448
1557-9654
DOI:10.1109/18.79910