Isotropic-polyharmonic B-splines and wavelets

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.

• Type: Conference
• Year: 2004
• Where: ICIP
• Authors: Dimitri Van De Ville, Thierry Blu, Brigitte Forster, Michael Unser
• Keywords: ICIP 2004, Image Processing, Isotropic Polyharmonic B-splines, Isotropic-polyharmonic B-spline Wavelet, Quincunx Subsampling Scheme, Single Wavelet, Two-dimensional Wavelet Bases