Cooperative Effects of a Parity-check Code on the Simultaneous Restoration of Two Images

In this study, we consider the simultaneous image restoration of two original images. We propose a model and examine the stationary state and dynamical properties of image restoration. To restore two images simultaneously, we assume that their parity-check code is composed of two pixels: one selected from the first image and the other from the second image. For the stationary state, we apply the replica method to obtain the equation of self-consistent order parameters. Meanwhile, for the dynamical properties of image restoration, we apply the path-integral approach. We demonstrate that the parity-check code cooperatively influences the restoration of two images; the performance of image restoration for a lower (higher) ordered image can be enhanced (suppressed) by another image through a parity-check code. The mechanism of the cooperative effect of the parity-check code on simultaneous image restoration is discussed, and a practical application of our model is proposed.