Journal of Algorithms
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
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
Estimating Crossing Fibers: A Tensor Decomposition Approach
IEEE Transactions on Visualization and Computer Graphics
Adaptive Kernels for Multi-fiber Reconstruction
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
Tensor Decompositions and Applications
SIAM Review
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
ODF maxima extraction in spherical harmonic representation via analytical search space reduction
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Symmetric positive-definite cartesian tensor orientation distribution functions (CT-ODF)
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Multi-diffusion-tensor fitting via spherical deconvolution: a unifying framework
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Maximum entropy spherical deconvolution for diffusion MRI
IPMI'05 Proceedings of the 19th international conference on Information Processing in Medical Imaging
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
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Fundamental to high angular resolution diffusion imaging (HARDI), is the estimation of a positive-semidefinite orientation distribution function (ODF) and extracting the diffusion properties (e.g., fiber directions). In this work we show that these two goals can be achieved efficiently by using homogeneous polynomials to represent the ODF in the spherical deconvolution approach, as was proposed in the Cartesian Tensor-ODF (CT-ODF) formulation. Based on this formulation we first suggest an estimation method for positive-semidefinite ODF by solving a linear programming problem that does not require special parameterization of the ODF. We also propose a rank-k tensor decomposition, known as CP decomposition, to extract the fibers information from the estimated ODF. We show that this decomposition is superior to the fiber direction estimation via ODF maxima detection as it enables one to reach the full fiber separation resolution of the estimation technique. We assess the accuracy of this new framework by applying it to synthetic and experimentally obtained HARDI data.