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arXiv · cond-mat/9902312

Statistical mechanics of image restoration and error-correcting codes

H. Nishimori·K. Y. M. Wong
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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.

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BibTeXRIS

H. Nishimori, K. Y. M. Wong. 1999-02-23. Statistical mechanics of image restoration and error-correcting codes. https://doi.org/10.1103/physreve.60.132

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