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2-D Spectrum estimation for imperfectly observed lattice data

In this paper we investigate the use of parametric models and robustified maximum likelihood to estimate two-dimensional power spectra from imperfectly observed lattice data. The maximum likelihood (ML) estimates for the signal plus noise model are consistent and asymptotically efficient for noncausal autoregressive (NCAR) models, but the solution requires the use of computationally expensive non-linear optimization, such as Newton-Raphson. By approximating the ML equations through the use of a toroidal lattice the computational complexity is reduced without unduly destroying the asymptotic properties of the estimates. When outliers in the data occurs, ML might not perform well. In this case we make no strict assumption about the distribution of the observations but assume only that the data are nominally Gaussian but with heavier tails. Then we use a robust procedure to estimate the parameters for the model.