American Institute of Mathematical Sciences

May  2013, 7(2): 565-583. doi: 10.3934/ipi.2013.7.565

Total variation and wavelet regularization of orientation distribution functions in diffusion MRI

 1 Department of Mathematics, University of Florida, Gainesville, FL 32611, United States 2 Center for Advanced Imaging, Evanston Hospital, 2650 Ridge Avenue, Evanston, IL 60201, United States

Received  October 2011 Revised  August 2012 Published  May 2013

We introduce a variational model and a numerical method for simultaneous ODF smoothing and reconstruction. The model uses the sparsity of MR images in finite difference domain and wavelet domain as the spatial regularization means in ODF's reconstruction. The model also incorporates angular regularization using Laplace-Beltrami operator on the unit sphere. A primal-dual scheme is applied to solve the model efficiently. The experimental results indicate that with spatial and angular regularization in the process of reconstruction, we can get better directional structures of reconstructed ODFs.
Citation: Yuyuan Ouyang, Yunmei Chen, Ying Wu. Total variation and wavelet regularization of orientation distribution functions in diffusion MRI. Inverse Problems & Imaging, 2013, 7 (2) : 565-583. doi: 10.3934/ipi.2013.7.565
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References:
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