Discrete fast algorithms for two-dimensional linear prediction on a polar raster

Discrete generalized split Levinson and Schur algorithms for the two-dimensional linear least-squares prediction problem on a polar raster are derived. The algorithms compute the prediction filter for estimating a random field at the edge of a disk from noisy observations inside the disk. The covariance functions of the random field is assumed to have a Toeplitz-plus-Hankel structure for its radial part and its transverse part. This assumption can be shown to be closely related with some types of random fields, such as isotropic random fields. The algorithms generalized the split Levinson and Schur algorithms in two ways: (1) to two dimensions; and (2) to Toeplitz-plus-Hankel covariances