A unified framework for estimating diffusion tensors of any order with symmetric positive-definite constraints

Authors:
Angelos Barmpoutis;Baba C. Vemuri
Affiliations:
The University of Florida, Department of Computer and Information Science and Engineering, Gainesville, Florida;The University of Florida, Department of Computer and Information Science and Engineering, Gainesville, Florida
Venue:
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Year:
2010

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Abstract

Cartesian tensors of various orders have been employed for either modeling the diffusivity or the orientation distribution function in Diffusion-Weighted MRI datasets. In both cases, the estimated tensors have to be positive-definite since they model positive-valued functions. In this paper we present a novel unified framework for estimating positive-definite tensors of any order, in contrast to the existing methods in literature, which are either order-specific or fail to handle the positive-definite property. The proposed framework employs a homogeneous polynomial parametrization that covers the fuIl space of any order positive-definite tensors and explicitly imposes the positive-definite constraint on the estimated tensors. We show that this parametrization leads to a linear system that is solved using the non-negative least squares technique. The framework is demonstrated using synthetic and real data from an excised rat hippocampus.