Determination of Fiber Orientation in MRI Diffusion Tensor Imaging Based on Higher-Order Tensor Decomposition

High angular resolution diffusion imaging (HARDI) techniques have been used for resolving multiple fiber directions within a voxel. Using HARDI, a high-order tensor can be obtained through generalized diffusion tensor imaging (GDTI). In this paper, based on the decomposition of the high-order diffusion tensors, a mathematical technique is presented which permits accurate resolution of multiple, randomly-oriented fiber tracts within tissue. A sequence of pseudo-eigenvalues and pseudo-eigenvectors are derived from the diffusion tensor through successive application of a best least-square rank-1 tensor approximation. These pseudo-eigenvalues and pseudo-eigenvectors are used to identify the major fiber directions within an individual image voxel. Results of a numerical simulation are presented to demonstrate the technique.