Image restoration using the Q-Ising spin glass.

We investigate static and dynamic properties of gray-scale image restoration by making use of the Q-Ising spin glass model, whose ladder symmetry allows us to take in account the distance between two spins. We thus give an explicit expression of the Hamming distance between the original and restored images as a function of the hyperparameters in the mean field limit. Finally, numerical simulations for real-world pictures are carried out to prove the efficiency of our model.

Image restoration using the chiral Potts spin glass.

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which cannot be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three-gray-scale-level case. In order to check our analytical result and the efficiency of our model, two-dimensional Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.