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Title: Estimation theory and statistical physics. Technical paper

Abstract

The construction of a nonlinear filter involves an integration over function space which is exactly analogous to the construction of a measure on path space via the Feynman-Kac-Nelson formula. In Kalman-Bucy filtering problem the filtering of Gauss-Markov processes in the presence of additive white Gaussian noise occupies the same role as the Ornstein-Uhlenbeck process (finite or infinite-dimensional) in quantum mechanics or quantum field theory. That this analogy is borne out by the fact that a solvable Lie algebra, the oscillator algebra which contains the Heisenberg algebra as a derived algebra is intrinsically attached to the Kalman-Bucy filtering problem. The problem of nonlinear filtering of diffusion processes was shown to admit a stochastic variational interpretation. The objective of this paper is to strengthen these analogies further with a view to showing the close relationship of estimation theory to statistical mechanics. The motivation for this comes from problems of estimation and inverse problems related to image processing. In order to carry out this program it is necessary to generalize these ideas to filtering problems for infinite-dimensional processes. There are two types of processes involved: continuous processes such as infinite-dimensional Ornstein-Uhlenbeck processes and their L2-functionals which represent intensities of images and processes ofmore » a discrete nature which will represent boundaries of images. The most interesting models are obtained when these processes are coupled according to a probabilistic mechanisms. The discrete processes should be thought of as gauge fields and will be a process on connection forms.« less

Authors:
Publication Date:
Research Org.:
Massachusetts Inst. of Tech., Cambridge (USA). Lab. for Information and Decision Systems
OSTI Identifier:
5629112
Report Number(s):
AD-A-164054/9/XAB; LIDS-P-1518
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; LIE GROUPS; STATISTICAL MECHANICS; VARIATIONAL METHODS; ALGEBRA; DIFFUSION; FUNCTIONALS; IMAGE PROCESSING; PROBABILITY; STATISTICS; FUNCTIONS; MATHEMATICS; MECHANICS; PROCESSING; SYMMETRY GROUPS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics; 645400 - High Energy Physics- Field Theory

Citation Formats

Mitter, S K. Estimation theory and statistical physics. Technical paper. United States: N. p., 1985. Web.
Mitter, S K. Estimation theory and statistical physics. Technical paper. United States.
Mitter, S K. 1985. "Estimation theory and statistical physics. Technical paper". United States.
@article{osti_5629112,
title = {Estimation theory and statistical physics. Technical paper},
author = {Mitter, S K},
abstractNote = {The construction of a nonlinear filter involves an integration over function space which is exactly analogous to the construction of a measure on path space via the Feynman-Kac-Nelson formula. In Kalman-Bucy filtering problem the filtering of Gauss-Markov processes in the presence of additive white Gaussian noise occupies the same role as the Ornstein-Uhlenbeck process (finite or infinite-dimensional) in quantum mechanics or quantum field theory. That this analogy is borne out by the fact that a solvable Lie algebra, the oscillator algebra which contains the Heisenberg algebra as a derived algebra is intrinsically attached to the Kalman-Bucy filtering problem. The problem of nonlinear filtering of diffusion processes was shown to admit a stochastic variational interpretation. The objective of this paper is to strengthen these analogies further with a view to showing the close relationship of estimation theory to statistical mechanics. The motivation for this comes from problems of estimation and inverse problems related to image processing. In order to carry out this program it is necessary to generalize these ideas to filtering problems for infinite-dimensional processes. There are two types of processes involved: continuous processes such as infinite-dimensional Ornstein-Uhlenbeck processes and their L2-functionals which represent intensities of images and processes of a discrete nature which will represent boundaries of images. The most interesting models are obtained when these processes are coupled according to a probabilistic mechanisms. The discrete processes should be thought of as gauge fields and will be a process on connection forms.},
doi = {},
url = {https://www.osti.gov/biblio/5629112}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Dec 01 00:00:00 EST 1985},
month = {Sun Dec 01 00:00:00 EST 1985}
}

Technical Report:
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