title: Robust 4D flow denoising using divergence-free wavelet transform.
abstract: OBJECTIVE
  To investigate four-dimensional flow denoising using the divergence-free wavelet (DFW) transform and compare its performance with existing techniques.
  
  
  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.
  
  
  CONCLUSIONS
  DFW denoising of four-dimensional flow data was shown to reduce noise levels in flow data both quantitatively and visually.
authors.affiliation: Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California, USA.
authors.forename: Frank
authors.initials: F
authors.lastname: Ong
authors.forename: Martin
authors.initials: M
authors.lastname: Uecker
authors.forename: Umar
authors.initials: U
authors.lastname: Tariq
authors.forename: Albert
authors.initials: A
authors.lastname: Hsiao
authors.forename: Marcus T
authors.initials: MT
authors.lastname: Alley
authors.forename: Shreyas S
authors.initials: SS
authors.lastname: Vasanawala
authors.forename: Michael
authors.initials: M
authors.lastname: Lustig
mesh_terms: D000465:Algorithms; D016477:Artifacts; D001783:Blood Flow Velocity / Q000502:physiology*; D002648:Child; D003326:Coronary Circulation / Q000502:physiology*; D005260:Female; D006801:Humans; D007089:Image Enhancement / Q000379:methods; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D018810:Magnetic Resonance Angiography / Q000379:methods*; D008297:Male; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio; D058067:Wavelet Analysis
keywords: divergence-free; four-dimensional flow; wavelet denoising