Journal of Mathematical Imaging and Vision
Symmetric positive 4th order tensors & their estimation from diffusion weighted MRI
IPMI'07 Proceedings of the 20th international conference on Information processing in medical imaging
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
A New Tensorial Framework for Single-Shell High Angular Resolution Diffusion Imaging
Journal of Mathematical Imaging and Vision
Higher Order Positive Semidefinite Diffusion Tensor Imaging
SIAM Journal on Imaging Sciences
Large deformation diffeomorphic metric mapping of orientation distribution functions
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Journal of Mathematical Imaging and Vision
Approximating Symmetric Positive Semidefinite Tensors of Even Order
SIAM Journal on Imaging Sciences
Nonnegative Diffusion Orientation Distribution Function
Journal of Mathematical Imaging and Vision
Fast and analytical EAP approximation from a 4th-order tensor
Journal of Biomedical Imaging - Special issue on Advanced Signal Processing Methods for Biomedical Imaging
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DTI is an important tool to investigate the brain in vivoand non-invasively in spite of its shortcomings in regions of fiber-crossings. HARDI models such as QBI and Higher Order Tensors (HOT) were invented to overcome this shortcoming. HOTs, however, have not been explored extensively even though sophisticated estimation schemes were developed for DTI that guarantee positive diffusivity, such as the Riemannian framework. Positive diffusivity is an important constraint in diffusion MRI since it represents the physical phenomenon of molecular diffusion. It seems apt, to leverage the work done on DTI, to apply the positivity constraint to the HOT model. We, therefore, propose to extend the Riemannian framework from DTI to the space of 4th order diffusion tensors. We also review the existing methods for estimating 4th order diffusion tensors and compare all methods on synthetic, phantom and real datasets extensively to test for robustness and speed. Our contributions for extending the Riemannian framework from DTI to estimating 4th order diffusion tensors guarantees positive diffusivity, is robust, is fast, and can be used to discern multiple fiber directions.