Abstract
This paper deals with the estimation of a two-dimensional homogeneous random field with a separable autocovariance function. The optimal line-by-line filtering and smoothing algorithms are obtained by the use of a one-dimensional state-space representation for the random field derived from a two-dimensional model9) and the Kalman filtering theory. Then applying an orthogonal transform, the line-byline vector processing algorithms are decomposed into a set of scalar equations. The optimal scalar algorithms are implemented with the help of the standard fast Fourier transform. A simulation study by using artificial random field is demonstrated and an application to image processing is discussed to show the applicability of the present technique.
