Diffusion tensor image processing using biquaternions

We propose a biquaternion formalism to model diffusion tensor magnetic resonance imaging (DT-MRI) data. Unlike previous methods that use dimensionality reduction, we are able to process the full tensor in a holistic manner while respecting the underlying manifold of the data. Using this approach, we introduce the Fourier transform and convolution for DT-MRI for the first time, which can be applied directly on the full tensor. This opens up a wide range of applications for DT-MRI image processing. Further, based on this formulation, we present a biquaternion gradient vector and edge detector for DT images. Preliminary results of applying the Fourier transform, convolution and edge detector on synthetic examples as well as real DT data show great promise in our approach for DT image processing.