Solvable Markov random field model in color image restoration

We propose a scheme for image restoration of full color images by means of a solvable probabilistic model in the red-green-blue space. A special case of our solvable probabilistic model is equivalent to a multicomponent Gaussian model in the statistical mechanics. Exact closed expressions of the evidence and the expectation value of intensity at each pixel in our solvable probabilistic model can be obtained by using multidimensional Gaussian integral formulas and a discrete Fourier transform. In the present paper, the degradation process is assumed to be an additive white Gaussian noise. Hyperparameters are determined so as to maximize the evidence that is expressed in terms of the partition function in our solvable probabilistic model. This work is a pioneering work for the Bayesian approach to the color image restoration by means of the statistical-mechanical technique.