Regularizing Flows for Constrained Matrix-Valued Images
Journal of Mathematical Imaging and Vision
A Riemannian Framework for Tensor Computing
International Journal of Computer Vision
Journal of Mathematical Imaging and Vision
D-eigenvalues of diffusion kurtosis tensors
Journal of Computational and Applied Mathematics
On Computing the Underlying Fiber Directions from the Diffusion Orientation Distribution Function
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Riemannian Framework for Estimating Symmetric Positive Definite 4th Order Diffusion Tensors
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Impact of Rician Adapted Non-Local Means Filtering on HARDI
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Z-eigenvalue methods for a global polynomial optimization problem
Mathematical Programming: Series A and B
Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
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
Computational Optimization and Applications
Journal of Mathematical Imaging and Vision
On determinants and eigenvalue theory of tensors
Journal of Symbolic Computation
Estimation of non-negative ODFs using the eigenvalue distribution of spherical functions
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
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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Due to the well-known limitations of diffusion tensor imaging, high angular resolution diffusion imaging (HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient (ADC) with higher order diffusion tensors. The diffusivity function is positive semidefinite. In the literature, some methods have been proposed to preserve positive semidefiniteness of second order and fourth order diffusion tensors. None of them can work for arbitrarily high order diffusion tensors. In this paper, we propose a comprehensive model to approximate the ADC profile by a positive semidefinite diffusion tensor of either second or higher order. We call this the positive semidefinite diffusion tensor (PSDT) model. PSDT is a convex optimization problem with a convex quadratic objective function constrained by the nonnegativity requirement on the smallest Z-eigenvalue of the diffusivity function. The smallest Z-eigenvalue is a computable measure of the extent of positive definiteness of the diffusivity function. We also propose some other invariants for the ADC profile analysis. Experiment results show that higher order tensors could improve the estimation of anisotropic diffusion and that the PSDT model can depict the characterization of diffusion anisotropy which is consistent with known neuroanatomy.