Title :
Fast Computation of Polyharmonic B-Spline Autocorrelation Filters
Author :
Barbotin, Yann ; Van De Ville, Dimitri ; Blu, Thierry ; Unser, Michael
Author_Institution :
Biomed. Imaging Group, Ecole Polytech. Fed. de Lausanne, Lausanne
fDate :
6/30/1905 12:00:00 AM
Abstract :
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.
Keywords :
Fourier transforms; filtering theory; splines (mathematics); Fourier transform; approximation error; polyharmonic B-spline autocorrelation filters; polyharmonic splines; truncated-sum approach; Autocorrelation; Biomedical imaging; Educational institutions; Filters; Fourier transforms; Interpolation; Laplace equations; Multidimensional signal processing; Multidimensional systems; Spline; Autocorrelation sequence; Epstein zeta function; polyharmonic B-splines;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2008.2006714
