Isotropic-Polyharmonic BSplines and Wavelets
Dimitri Van De Ville, BIG, EPFL

Test Run • 19 October 2004 • BM 4.235

Abstract
We propose the use of polyharmonic B-splines to build non-separable two-dimensional wavelet bases. The central idea is to base our design on the isotropic polyharmonic B-splines, a new type of polyharmonic B-splines that do converge to a Gaussian as the order increases. We opt for the quincunx subsampling scheme which allows us to characterize the wavelet spaces with a single wavelet: the isotropic-polyharmonic B-spline wavelet. Interestingly, this wavelet converges to a combination of four Gabor atoms, which are well separated in frequency domain. We also briefly discuss our Fourier-based implementation and present some experimental results.