Restoration Process for Gray-scale Patterns by Using Path-integral

Abstract

We investigate a restoration process for a gray-scale pattern given by a snapshot of the Q-states ferromagnetic Husimi-Temperly model within a framework of a Bayesian inference. By using a generating function of pathintegral representation, we derive an equation which describes the restoration process for the gray-scale pattern. We investigate two systems: system 1 in which the gray-scale value takes on fÀ1; À1 þ 2 QÀ1 ; Á Á Á ; 1 À 2 QÀ1 ; 1g and system 2 in which the gray-scale value takes on f1; Á Á Á ; Qg. We find that there exists difference between Q ¼ 2 and Q ! 3 as for behavior of the restoration process for the system 1.