Bostan, Emrah
Unser, Michael
Ward, John Paul
Divergence-Free Wavelet Frames
Ieee Signal Processing Letters
1070-9908
10.1109/Lsp.2015.2388794
22
8
1142-1146
5
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.
Denoising;
divergence-free wavelets;
flow MRI;
phase-contrast MRI;
soft-thresholding;
tight wavelet frames;
vector fields;
vector wavelets;
wavelet denoising;
Ieee-Inst Electrical Electronics Engineers Inc
Piscataway
2015
http://bigwww.epfl.ch/publications/bostan1502.html;
http://bigwww.epfl.ch/publications/bostan1502.pdf;
http://bigwww.epfl.ch/publications/bostan1502.ps;