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Robust 4D flow denoising using divergence‐free wavelet transform
Author(s) -
Ong Frank,
Uecker Martin,
Tariq Umar,
Hsiao Albert,
Alley Marcus T,
Vasanawala Shreyas S.,
Lustig Michael
Publication year - 2015
Publication title -
magnetic resonance in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.696
H-Index - 225
eISSN - 1522-2594
pISSN - 0740-3194
DOI - 10.1002/mrm.25176
Subject(s) - noise reduction , discretization , wavelet , computer science , divergence (linguistics) , noise (video) , artificial intelligence , wavelet transform , pattern recognition (psychology) , flow (mathematics) , mathematics , computer vision , mathematical analysis , linguistics , philosophy , geometry , image (mathematics)
Purpose To investigate four‐dimensional flow denoising using the divergence‐free wavelet (DFW) transform and compare its performance with existing techniques. Theory and Methods DFW is a vector‐wavelet that provides a sparse representation of flow in a generally divergence‐free field and can be used to enforce “soft” divergence‐free conditions when discretization and partial voluming result in numerical nondivergence‐free components. Efficient denoising is achieved by appropriate shrinkage of divergence‐free wavelet and nondivergence‐free coefficients. SureShrink and cycle spinning are investigated to further improve denoising performance. Results DFW denoising was compared with existing methods on simulated and phantom data and was shown to yield better noise reduction overall while being robust to segmentation errors. The processing was applied to in vivo data and was demonstrated to improve visualization while preserving quantifications of flow data. Conclusion DFW denoising of four‐dimensional flow data was shown to reduce noise levels in flow data both quantitatively and visually. Magn Reson Med 73:828–842, 2015. © 2014 Wiley Periodicals, Inc.