We report on the restoration of gray-scale image when it is decomposed into a binary form before transmission. We assume that a gray-scale image expressed by a set of Q-Ising spins is first decomposed into an expression using Ising (binary) spins by means of the threshold division, namely, we produce $\left(Q-1\right)$ binary Ising spins from a Q-Ising spin by the function $F\left({\sigma }_i-m\right)=1\mathrm{}$ if the input data ${\sigma }_i\in \{0,\dots ,Q-1\}$ is ${\sigma }_i>~m$ and 0 otherwise, where m $\in \{1,\dots ,Q-1\}$ is the threshold value. The effects of noise are different from the case where the raw Q-Ising values are sent. We investigate whether it is more effective to use the binary data for transmission, or to send the raw Q-Ising values. By using the mean-field model, we analyze the performance of our method quantitatively. In order to investigate what kind of original picture is efficiently restored by our method, the standard image in two dimensions is simulated by the mean-field annealing, and we compare the performance of our method with that using the Q-Ising form. We show that our method is more efficient than the one using the Q-Ising form when the original picture has large parts in which the nearest-neighboring pixels take close values.

• Received 20 May 2001

DOI:https://doi.org/10.1103/PhysRevE.65.016101