On Diffusion Tensor Estimation

M. Niethammer, R. San Jose Estepar, S. Bouix, M. E. Shenton, C.-F. Westin
28th IEEE EMBS
Pages 2622-2625
September, 2006

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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.

Coronal slice of a real human brain. Indefinite tensors appear in the corpus callosum and yield higher than expected planar measures (see circles).The proposed method leads to a visibly smoother estimation of the planar measure within the highly anisotropic corpus callosum.

Reference

Niethammer M, San Jose Estepar R, Bouix S, Shenton M, Westin CF. On diffusion tensor estimation. In 28th IEEE EMBS. New York City, NY, USA, 2006;2622-2625.

Bibtex entry

@InProceedings{niethammerEMBS06,
  author         = {Niethammer, M. and {San Jose Estepar}, Raul and Bouix,     
                   Sylvain  and Shenton, Martha and Westin, C.-F. },           
  title          = {On Diffusion Tensor Estimation},                           
  booktitle      = {28th IEEE EMBS},                                           
  year           = {2006},                                                     
  pages          = {2622--2625},                                               
  address        = {New York City, NY, USA},                                   
  month          = {September}
}

Grants

NIH U54-EB005149 (NAMIC), NIH R01-MH50747, NIH K05-70047

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