A Joint PDF for the Eigenvalues and Eigenvectors of a Diffusion Tensor

Sinisa Pajevic¹, Peter J. Basser²

We propose a joint probability density function (pdf) of the eigensystem of a 2nd-order estimated diffusion tensor, which we show decouples into a product of pdfs of its eigenvalues and eigenvectors for a well-designed MR experiment and moderate SNR. This finding provides the foundation for the development of a rigorous and general statistical hypothesis-testing framework valid for measured DTI data.