### Abstract

Dynamical properties of image restoration and hyper-parameter estimation are investigated by means of statistical mechanics. We introduce an exactly solvable model for image restoration and derive the differential equations with respect to macroscopic quantities. From these equations, we evaluate relaxation processes of the system to its equilibrium state in the sense of the Markov chain Monte Carlo (MCMC) method. Our statistical mechanical approach also enable one to investigate the hyper-parameter estimation by means of maximization of marginal likelihood using gradient decent, or the EM algorithm from dynamical point of view.

Original language | English |
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Pages | 383-392 |

Number of pages | 10 |

Publication status | Published - 2001 Dec 1 |

### ASJC Scopus subject areas

- Signal Processing
- Software
- Electrical and Electronic Engineering

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## Cite this

Inoue, J. I., & Tanaka, K. (2001).

*Dynamical properties of image restoration and hyper-parameter estimation*. 383-392.