Optimal lattices for interpolation of stationary random fields

Hans R. Künsch, Erik Agrell and Fred A. Hamprecht

August 2003

Abstract

We consider interpolation of a stationary random field that has been observed on a lattice. Exact expressions for the mean square error of the best linear unbiased estimator are given in the frequency domain. Morevoer, we derive asymptotic expansions of the average mean square error when the sampling rate tends to zero and to infinity respectively. This allows us to determine the optimal lattices for interpolation. In the low-rate sampling case, or equivalently for rough processes, the optimal lattice is the one which solves the packing problem, whereas in the high-rate sampling case, or equivalently for smooth surfaces, the optimal lattice is the one which solves the dual packing problem. In addition, we compare the best linear unbiased interpolation with cardinal interpolation.

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