Generalized Levinson and fast Cholesky algorithms for three-dimensional random field estimation problems

Fast algorithms for computing the linear least-squares estimate of a three-dimensional random field from noisy observations inside a sphere are derived. The algorithms can be viewed as generalized split Levinson and fast Cholesky algorithms, since they exploit the (assumed) Toeplitz structure of the double Radon transform of the random field covariance, and therefore they require fewer computations than would solution of the multidimensional Wiener-Hopf equation. Unlike previous generalized Levinson algorithms, no quarter-plane or asymmetric half-plane support assumptions for the filter are necessary; nor is the multidimensional filtering problem treated as a multichannel (vector) filtering problem