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

New 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 function of the random field is assumed to have a Toeplitzplus-Hankel structure for both its radial part and its transverse (angular) part. This assumption is valid for some types of random fields, such as isotropic random fields. The algorithms generalize the split Levinson and Schur algorithms in two ways: 1) to two dimensions; and 2) to Toeplitz-plus-Hankel covariances.