Linear Interpolation Theory for Multidimensional Identification and Estimation

Motivated by the rational modeling problem in multidimensional spectrum estimation, we generalize some results from linear prediction theory to multiple dimensions. Non-causal models are needed for spectrum estimation algorithms in multiple dimensions because causal models do not generate the complete class of rational m-D spectra. Innovations are defined for non-causal prediction and the innovations representation for non-causally regular random fields is developed. In addition, we formulate and prove a spatial domain Wold decomposition theorem for random fields and relate the decomposition to the random field´s frequency domain representation. Using the non-causal, innovations driven model we derive a spectrum estimation algorithm based upon a definition of state for non-causal rational systems.