Statistical mechanics of image restoration and error-correcting codes

Details Statistical mechanics of image restoration and error-correcting codes Statistical mechanics of image restoration and error-correcting codes

1999-02-23

arxiv.org/abs/cond-mat/9902312v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

20 pages, 9 figures, ReVTeX

Scientific paper

10.1103/PhysRevE.60.132

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.

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