Robust 4D flow denoising using divergence-free wavelet transform


  • This article was presented in part at the 21st annual meeting of ISMRM, Salt Lake City, Utah, 2013, the annual meeting of ISBI, San Francisco, California, 2013, and the annual meeting of SCMR, San Francisco, California, 2013.



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.


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.


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.