Anisotropy of HARDI Diffusion Profiles Based on the L2-Norm
The fractional anisotropy (FA) value for Diffusion Tensor Imaging is widely used to determine the anisotropy of diffusion in a given voxel. As the FA value is based on the tensor’s eigenvectors it is not possible to calculate this quantity for HARDI diffusion profiles. In this paper we introduce an anisotropy index for HARDI data that utilizes the L2-norm as the most natural notion of distance for square-integrable functions on the two-sphere such as HARDI diffusion profiles and show that it is the limit of the generalized fractional anisotropy (GFA) index. Our index is well-defined and rotationally invariant and thus resolves the unsatisfactory issues with the GFA index.
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