Isotropic-polyharmonic B-splines and wavelets (MP-L3)

Author(s) : Dimitri Van De Ville (Swiss Federal Institute of Technology Lausanne, Switzerland) Thierry Blu (Swiss Federal Institute of Technology Lausanne, Switzerland) Brigitte Forster (Swiss Federal Institute of Technology Lausanne, Switzerland) Michael Unser (Swiss Federal Institute of Technology Lausanne, Switzerland)

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.

Menu