Total variation and wavelet regularization of orientationdistribution functions in diffusion MRI

Yuyuan Ouyang; Yunmei Chen; Ying Wu

doi:10.3934/ipi.2013.7.565

Article Contents

2013, Volume 7, Issue 2: 565-583. Doi: 10.3934/ipi.2013.7.565

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

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

Received: September 30, 2011

Revised: July 31, 2012

Published: April 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 92C55; Secondary: 15A29.

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