On the basis of statistical mechanics formulation for problems of image restoration and error-correcting codes, we propose a new technique of image restoration for a binary image using the plane rotator model. In our formulation, the restored image is obtained from the equilibrium state of a ferromagnetic plane rotator model under a random field which consists of the corrupted image at finite temperature. The validity of our technique is evaluated by the dependence of overlap on the hyperparameters using the replica symmetric theory for the infinite-range model. The theory shows that our technique achieves the same optimal performance with that by the Ising spins. This statement is qualitatively confirmed by Monte Carlo simulations for two-dimensional images. Furthermore we estimate the dynamics of our technique by using Monte Carlo simulations. The simulations reveal that the convergence to the restored image is faster than that by the Ising model at low temperature.
ASJC Scopus subject areas
- Physics and Astronomy(all)