  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.
