Anisotropic Kernel Smoothing in Diffusion Tensor Imaging


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.