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 path-integral 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 {−1,−1+
2/
(Q−1),···,1−
2/
(Q−1),1} and system 2 in which the gray-scale value takes on {1,···,
Q}. We find that there exists difference between
Q=2 and
Q≥3 as for behavior of the restoration process for the system 1.
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