TY - EJOUR
DO - 10.1109/Lsp.2015.2388794
AB - 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.
T1 - Divergence-Free Wavelet Frames
IS - 8
DA - 2015
AU - Bostan, Emrah
AU - Unser, Michael
AU - Ward, John Paul
JF - Ieee Signal Processing Letters
SP - 1142-1146
VL - 22
EP - 1142-1146
PB - Ieee-Inst Electrical Electronics Engineers Inc
PP - Piscataway
ID - 205283
KW - Denoising
KW - divergence-free wavelets
KW - flow MRI
KW - phase-contrast MRI
KW - soft-thresholding
KW - tight wavelet frames
KW - vector fields
KW - vector wavelets
KW - wavelet denoising
SN - 1070-9908
UR - http://bigwww.epfl.ch/publications/bostan1502.html
UR - http://bigwww.epfl.ch/publications/bostan1502.pdf
UR - http://bigwww.epfl.ch/publications/bostan1502.ps
ER -