Dynamical properties of image restoration and hyper-parameter estimation

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 enables one to investigate the hyper-parameter estimation by means of maximization of marginal likelihood using gradient descent, or the EM algorithm from dynamical point of view.