Bandwidth Optimization for Compact Fourier Interpolation

In this paper, we present a bandwidth-optimization technique for Compact Fourier Interpolation (COMFI). COMFI is a minimum mean-square-error interpolation technique for data sampled at irregular locations. A particular application of interpolation is the estimation of data on a global, Cartesian grid (regularization). The sampling space can be of arbitrary dimension. The interpolated data are computed as a weighted sum of the actual data in a neighbourhood of the selected interpolation locations. The interpolation operator depends on the actual sampling locations and the interpolation location, but not on the data themselves. The operator is designed to have the minimum mean-square interpolation error among all linear operators over a suitable class of spatially band-limited basis functions. We consider, however, the spatial bandwidth as a parameter to be selected in an optimum way. Typically, we compute the COMFI operator to have the largest bandwidth that the actual sampling regime supports, in the sense that the mean-square interpolation error is below an acceptable threshold. We show that the quality of the operator can be strongly dependent on the bandwidth used for its design, and that the optimum bandwidth can vary significantly with spatial location.