Fast Computation of Polyharmonic B-Spline Autocorrelation Filters

A fast computational method is given for the Fourier transform of the polyharmonic B-spline autocorrelation sequence in d dimensions. The approximation error is exponentially decaying with the number of terms taken into account. The algorithm improves speed upon a simple truncated-sum approach. Moreover, it is virtually independent of the spline's order. The autocorrelation filter directly serves for various tasks related to polyharmonic splines, such as interpolation, orthonormalization, and wavelet basis design.