Digital linear processor theory and optimum multidimensional data estimation

This paper introduces frame recursive processing as a new algoritlun for processing of blurred or unblurred pictorial information with additional noise. It gives an improved image which approaches optimum in the least mean square error sense. The method represents a new direction in two-dimensional digital filtering from the current trend of using generating equations and a Kalman filter which requires artificial introduction of a causal order of data points. Applications include two-dimensional image restoration, three-dimensional image reconstruction from two-dimensional cross sections, and real-time image processing of a moving object. In all cases the optimum linear processor utilizes all available information on the second statistical moments to give the least mean square error, and is realized by frame recursive processing in successive approximation with an exponentially decaying error. A fast hardware realization of the frame processor is also proposed.