Efficient and Effective Anisotropic Smoothing of Diffusion Tensor Images in Log-Euclidean Framework

Qing Xu¹, Adam W. Anderson¹, John C. Gore¹, Zhaohua Ding¹

We present a technique to denoise diffusion tensor images by performing non-iterative anisotropic smoothing in the Log-Euclidean framework. The diffusion tensors are first transformed to tensor logarithm space to perform Euclidean computing for vectors. Then an anisotropic smoothing algorithm for multi-channel image is implemented with an unconditionally stable and second order accurate semi-implicit scheme, which allows us to choose large step size and thus use one iteration to achieve optimal effect. The tests with in vivo DTI data have demonstrated that there is up to 50% improvement on the principal diffusion directions with one iteration of anisotropic filtering.