1070-9908
Divergence-Free Wavelet Frames
Bostan
Emrah
Unser
Michael
Ward
John Paul
2015
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.
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