Geometric kernel smoothing of tensor fields

In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor field on the performance of different smoothers arising from using different metrics, viz., Euclidean, log-Euclidean and affine invariant metrics. We also study the Rician noise model and compare two regression estimators of diffusion tensors based on raw diffusion weighted imaging data at each voxel.