EPFL | Biomedical Imaging Group | Divergence-Free Wavelets

Divergence-Free Wavelet Frames

E. Bostan, M. Unser, J.P. Ward

2015 Twenty-Second IEEE International Conference on Image Processing (ICIP'15), Québec QC, Canada, September 27-30, 2015, TEC-P19.2.

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets retain the basic characteristics (decay rate and order of vanishing moments) of the initial wavelets. Since the Leray projector is also shift-invariant, it is defined as a Fourier multiplier, and our construction is implemented efficiently using the fast Fourier transform. In order to illustrate the practicality of the method, we present vector field denoising experiments.

This abstract was originally published as E. Bostan, M. Unser, J.P. Ward, "Divergence-Free Wavelet Frames," IEEE Signal Processing Letters, vol. 22, no. 8, pp. 1142-1145, August 2015.

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