One-sided recursive filters for two-dimensional random fields (Corresp.)

The one-sided (or line-by-line) recursive filtering problem for a two-parameter Gaussian random signal in additive white Gaussian noise is considered. For a reasonably large class of models for the signal dynamics, both the filtering equation and the generalized Riccati equation explicitly obtained. As an example, the Riccati equation is solved to give the filter gain in a time-in-variant case and is compared with the infinite-time limiting solution to the Wiener filter solution obtained by spectral factorization techniques.