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.
Keywords: divergence-free; four-dimensional flow; wavelet denoising.
© 2014 Wiley Periodicals, Inc.