Realizable Wiener filtering in two dimensions

The extension of Wiener´s classical mean-square estimation theory to a two-dimensional setting is presented. In analogy with the one-dimensional problem, the optimal realizable filter is derived by solution of a two-dimensional, discrete Wiener-Hopf equation using a spectral factorization procedure. Filters are developed for the cases of prediction, filtering, and smoothing, and appropriate error expressions are derived to characterize their performance.