Title :
Stochastic cellular automata with Gibbsian invariant measures
Author :
Marroquín, José Luis ; Ramírez, Arturo
Author_Institution :
Centro de Investigacion en Math., Guanajuato, Mexico
fDate :
5/1/1991 12:00:00 AM
Abstract :
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.
Keywords :
Markov processes; finite automata; stochastic processes; Cartesian product; Gibbsian distributions; Gibbsian invariant measures; Markovian random fields; convex polytopes; convex programming; geometric characterization; image restoration problems; invariant probability measures; nonreversible dynamic behavior; optimal automata; stochastic cellular automata; Automata; Automatic programming; Bayesian methods; Computational modeling; Image restoration; Lattices; Markov random fields; Probability distribution; Stochastic processes; Stochastic systems;
Journal_Title :
Information Theory, IEEE Transactions on