**Anisotropic Kernel Smoothing in
Diffusion
Tensor Imaging**

**Description **

Diffusion
tensor imaging (DTI)
provides the directional information of water molecule diffusion in the
white
matter of the human brain. It is usually represented as the collection
of 6
multivariate images that represent a 3 by 3 symmetric positive definite
matrix
called diffusion coefficients. The diffusion coefficients can be used
to
understand the pattern of white fibers in the brain. Most previous
regularization works on diffusion tensor magnetic resonance images have
been
based on either anisotropic heat equations or streamline approaches. We
present
a novel regularization method using iterated anisotropic kernels that
avoids
solving diffusion equations or streamline equations while improves upon
numerical stability. The bandwidth of kernel is proportionally matched
to the
diffusion tensor to smooth out more along the tensor fields. The
proportionally
constant is chosen to minimize the sum of the squared intensity
difference between before and after smoothing
while maximizing the smoothness of the image. The kernel method
can be
shown to increases the signal-to-noise ratio while preserving the
anisotropy of
the tensor fields. This formulation can be shown to be equivalent to
the edge
enhancing diffusion equation approaches.

Publications

- Lee, J.E. Chung, M.K., Hsu, D.,
Alexander, A.L. 2007. Probabilistic connectivity using
Kullback-Leibler distance, International Socieity for Magnetic
Resonance in Medicine (ISMRM) conference. Poster

- Lee, J.E., Chung, M.K., Alexander, A.L. 2006. Evaluation of
anisotropic filters for diffusion tensor imaging. IEEE International Symposium on Biomedical
Imaging (ISBI) 1241
- Lee, J.E., Chung, M.K., Alexander, A.L. 2006. Evaluation of anisotropic filtering
for DTI as a function of SNR. Proceedings of the 14th ISMRM
Scientific meeting.
- Lee, J.H., Chung, M.K., Oakes, T.E., Alexander,
A.L. 2005. Anisotropic
Gaussian kernel smoothing of DTI data. 13th Meeting of
International Society for Magnetic Resonance in Medicine. 2253.
- Chung, M.K., Lazar, M., Alexander, A.L., Lu., Y.,
Davidson, R. 2003. Probabilistic
Connectivity Measure in Diffusion Tensor Imaging via Anisotropic Kernel
Smoothing, Technical Report
1081. Department of Statististics, Universisty of
Wisconsin-Madison.
- Chung, M.K., Alexander, A.L., Lu, Y. 2003. Connection
Probability in Diffusion Tensor Imaging via Anisotropic Gaussian Kernel
Smoothing, 9th Annual Meeting of the Organization for Human Brain
Mapping.