Statistical mechanics of image restoration and error-correcting codes
Abstract
We develop a statistical-mechanical formulation for image restoration and error-correcting codes. These problems are shown to be equivalent to the Ising spin glass with ferromagnetic bias under random external fields. We prove that the quality of restoration/decoding is maximized at a specific set of parameter values determined by the source and channel properties. For image restoration in mean-field system a line of optimal performance is shown to exist in the parameter space. These results are illustrated by solving exactly the infinite-range model. The solutions enable us to determine how precisely one should estimate unknown parameters. Monte Carlo simulations are carried out to see how far the conclusions from the infinite-range model are applicable to the more realistic two-dimensional case in image restoration.
Keywords
Cite
@article{arxiv.cond-mat/9902312,
title = {Statistical mechanics of image restoration and error-correcting codes},
author = {H. Nishimori and K. Y. M. Wong},
journal= {arXiv preprint arXiv:cond-mat/9902312},
year = {2009}
}
Comments
20 pages, 9 figures, ReVTeX