Iterated conditional modes for inverse dithering

Inverse dithering is to restore the original continuous-tone image from its dithering halftone. We propose to use iterated conditional modes (ICM) for approximating a maximum a posteriori (MAP) solution to the inverse problem. The statistical model on which the ICM is based takes advantage of the information on dither arrays. For the considered two common MRF's for measuring the smoothness of images, the corresponding energy functions are convex. The combination of this convexity and the structure of the constraint space associated with the MAP problem guarantees the global optimality. The ICM always searches the valid image space for a better estimate. There is no question of going beyond the valid space. In addition, it requires only local computation and is easy to implement. The experimental results show that the restored images have high quality. Compared with two previous DMI (dithering-model based inverse) methods, our ICM has higher PSNR's by 0.5-1.3 dB. The results also show that using the Gauss MRF (GMRF) for the continuous-tone image often had higher PSNR than using the Huber MRF (HMRF). An advantage of the GMRF is that it makes the ICM much easier to implement than the HMRF makes.