Two-dimensional linear prediction and spectral estimation on a polar raster

A zero-mean homogeneous random field is defined on a discrete polar raster. The problem is to estimate, given example values inside a disk of finite radius, the field´s power spectral density using linear prediction. A generalized autocorrelation procedure that guarantees positive semidefinite covariance estimates (required for a meaningful spectral density) is given. It first interpolates the data using Gaussians, computes its Radon transform, and applies familiar one-dimensional techniques to each slice. Some numerical examples are provided to justify the validity of the proposed procedure. A correlation matching covariance extension procedure that uses the Radon transform is proposed to extend a given set of covariance lags to the entire plane, when this is possible. Circumstances for which this is impossible are discussed