Bayesian Methods in Nonlinear Digital Image Restoration

Prior techniques in digital image restoration have assumed linear relations between the original blurred image intensity, the silver density recorded on film, and the film-grain noise. In this paper a model is used which explicitly includes nonlinear relations between intensity and film density, by use of the D-log E curve. Using Gaussian models for the image and noise statistics, a maximum a posteriori (Bayes) estimate of the restored image is derived. The MAP estimate is nonlinear, and computer implementation of the estimator equations is achieved by a fast algorithm based on direct maximization of the posterior density function. An example of the restoration method implemented on a digital image is shown.