Kazuyuki Tanaka et al 2004 J. Phys. A: Math. Gen. 37 8675 doi:10.1088/0305-4470/37/36/007
Kazuyuki Tanaka1, Hayaru Shouno2, Masato Okada3,4 and D M Titterington5
Show affiliationsWe investigate the accuracy of statistical-mechanical approximations for the estimation of hyperparameters from observable data in probabilistic image processing, which is based on Bayesian statistics and maximum likelihood estimation. Hyperparameters in statistical science correspond to interactions or external fields in the statistical-mechanics context. In this paper, hyperparameters in the probabilistic model are determined so as to maximize a marginal likelihood. A practical algorithm is described for grey-level image restoration based on a Gaussian graphical model and the Bethe approximation. The algorithm corresponds to loopy belief propagation in artificial intelligence. We examine the accuracy of hyperparameter estimation when we use the Bethe approximation. It is well known that a practical algorithm for probabilistic image processing can be prescribed analytically when a Gaussian graphical model is adopted as a prior probabilistic model in Bayes' formula. We are therefore able to compare, in a numerical study, results obtained through mean-field-type approximations with those based on exact calculation.
42.30.Va Image forming and processing
94A08 Image processing (compression, reconstruction, etc.) (See also 68U10)
Issue 36 (10 September 2004)
Received 16 February 2004, in final form 13 May 2004
Published 24 August 2004
Kazuyuki Tanaka et al 2004 J. Phys. A: Math. Gen. 37 8675
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