A telescoping approach to recursive enhancement of noisy images

Images are well modeled as noncausal random fields, i.e., fields where a pixel value depends on say, its four nearest neighbors. This noncausality creates problems when processing images since it preludes the application of recursive estimators, like the Kalman filter. This paper presents a new approach that allows the application of optimal Kalman filtering to random fields, while preserving the noncausality of the image random field model. The recursions in our approach are telescoping: they initiate at the periphery (or boundary) of the random field and telescope inwards. We show how to apply the new optimal recursive Kalman filter to enhancement of noisy images.