open access

https://hdl.handle.net/2115/44984

Construction of the maximizer of posterior marginal estimate by Langevin equation in probabilistic image processing

日本語

2011-03-24

2, 19 p.

We formulate the maximizer of posterior marginal (MPM) estimate for Bayesian probabilistic image processing by using the Langevin equation. We also evaluate the statistical performance from the view point of statistical mechanics of information. The multi-state Ising model and additive white Gaussian noise are introduced as the regularization term and the degrading process, respectively. Then, the recursion relations with respect to each pixel are derived via the extremum condition of energy function. The long-time average of time series derived from the recursion relations gives the maximum a posteriori (MAP) estimate and it is shown that the estimate is regarded as a kind of the average filter. We next try to construct the estimate using the fluctuation around the MAP estimate by solving stochastic differential equations and evaluate the performance both numerically and analytically. We perform an original image estimate by Markov chain Monte Carlo(MCMC) method numerically successively. Finally, we show that it is possible to construct the MPM estimate by simulating the Langevin equation numerically as well as the MCMC.

修士(情報科学)

修士論文

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