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Divergence-Free Wavelet Frames
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DOI：10.1109/LSP.2015.2388794.png)
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Abstract
En 中文
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.
Keywords:
Denoising
divergence-free wavelets
flow MRI
phase-contrast MRI
soft-thresholding
tight wavelet frames
vector fields
vector wavelets
wavelet denoising
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