American Institute of Mathematical Sciences

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November  2009, 3(4): 625-648. doi: 10.3934/ipi.2009.3.625

Variational denoising of diffusion weighted MRI

Tim McGraw 1, , Baba Vemuri 2, , Evren Özarslan 3, , Yunmei Chen 2, and  Thomas Mareci 2,

1. 

West Virginia University, Morgantown, WV 26506, United States
2. 

University of Florida, Gainesville, FL 32601, United States, United States, United States
3. 

National Institutes of Health, Bethesda, MD 20892, United States

Received  October 2008 Revised  August 2009 Published  October 2009

In this paper, we present a novel variational formulation for restoring high angular resolution diffusion imaging (HARDI) data. The restoration formulation involves smoothing signal measurements over the spherical domain and across the 3D image lattice. The regularization across the lattice is achieved using a total variation (TV) norm based scheme, while the finite element method (FEM) was employed to smooth the data on the sphere at each lattice point using first and second order smoothness constraints. Examples are presented to show the performance of the HARDI data restoration scheme and its effect on fiber direction computation on synthetic data, as well as on real data sets collected from excised rat brain and spinal cord.
Keywords: denoising., Diffusion MRI.
Mathematics Subject Classification: Primary: 92C55; Secondary: 62H3.
Citation: Tim McGraw, Baba Vemuri, Evren Özarslan, Yunmei Chen, Thomas Mareci. Variational denoising of diffusion weighted MRI. Inverse Problems and Imaging, 2009, 3 (4) : 625-648. doi: 10.3934/ipi.2009.3.625
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