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This report develops fast algorithms for computing filters for linear least squares estimation of one, two, and three dimensional random fields. The algorithms generalize the split Levinson and Schur algorithms to two and three dimensions; however, they are applicable to a more general Toeplitz plus Hankel structure in the covariance function. A discrete version of the Bellman Siegert Krein resolvent identity is developed for smoothing problems in one and two dimensions. Applications to linear predictive coding, and restoration and smoothing, of isotropic random fields on a polar raster are demonstrated. In addition, two new algorithms are developed for spectral estimation on a two- dimensional polar raster. Both use the Radon transform to map the two dimensional problem into one dimensional problems. Interpolating functions for computing the Radon transform, positive definite covariance extensions, and correlation matching are all considered.