Dynamical properties of algorithms for image restoration by means of Bayesian statistics

摘要

Recently, properties of image restoration were investigated in the context of Bayesian approach. However, these results are restricted to the static properties of the algorithms and no studies have ever tried to investigate these dynamical properties explicitly. In this report, we introduce an exactly solvable model for image restoration and derive the differential equation with respect to macroscopic quantities (Hamming distance between original and restored images, etc.) analytically. From these dynamical equations, we obtain useful information for image restoration, for example, basin of attraction, speed of convergence, etc. Our approach also enable one to investigate the hyper-parameter estimation by means of maximization of marginal likelihood using steepest descent from dynamical point of view.