BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Isotropic-Polyharmonic B-Splines and Wavelets

D. Van De Ville, T. Blu, B. Forster, M. Unser

Proceedings of the 2004 Eleventh IEEE International Conference on Image Processing (ICIP'04), Singapore, Singapore, October 24-27, 2004, pp. 661–664.

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. 

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