title: On diffusion tensor estimation.
abstract: In this paper we propose a formal formulation for the estimation of Diffusion Tensors in the space of symmetric positive semidefinite (PSD) tensors. Traditionally, diffusion tensor model estimation has been carried out imposing tensor symmetry without constraints for negative eigenvalues. When diffusion weighted data does not follow the diffusion model,due to noise or signal drop, negative eigenvalues may arise. An estimation method that accounts for the positive definiteness is desirable to respect the underlying principle of diffusion. This paper proposes such an estimation method and provides a theoretical interpretation of the result. A closed-form solution is derived that is the optimal data-fit in the matrix 2-norm sense,removing the need for optimization-based tensor estimation.
authors.affiliation: Department of Psychiatry, Brigham Women's Hospital, Harvard Medical School, Boston, MA, USA. marc@bwh.harvard.edu
authors.forename: Marc
authors.initials: M
authors.lastname: Niethammer
authors.forename: Raul San Jose
authors.initials: RS
authors.lastname: Estepar
authors.forename: Sylvain
authors.initials: S
authors.lastname: Bouix
authors.forename: Martha
authors.initials: M
authors.lastname: Shenton
authors.forename: Carl-Fredrik
authors.initials: CF
authors.lastname: Westin
mesh_terms: D000465:Algorithms; D016880:Anisotropy; D001921:Brain / Q000166:cytology / Q000502:physiology*; D004058:Diffusion; D006801:Humans; D010363:Pattern Recognition, Automated