Image restoration using the chiral Potts spin-glass

TL;DR

This paper introduces a novel image reconstruction method using a chiral Potts spin-glass model, demonstrating improved quality through analytical solutions and Monte Carlo simulations on real-world images with multiple gray-scale levels.

Contribution

The paper presents the first exact solution for the infinite range q=3 chiral Potts model applied to image restoration, enhancing previous models by incorporating glassy terms.

Findings

Glassy term improves image reconstruction quality.

Exact solution provided for the infinite range q=3 model.

Monte Carlo simulations confirm the model's effectiveness on real images.

Abstract

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 can not 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, 2D Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.