Bias of Least Squares Approaches for Diffusion Tensor Estimation from Array Coils in DT---MRI

Authors:
Antonio Tristán-Vega;Carl-Fredrik Westin;Santiago Aja-Fernández
Affiliations:
Laboratory of Image Processing, Universidad de Valladolid, Spain;LMI. Brigham and Women's Hospital, Boston;Laboratory of Image Processing, Universidad de Valladolid, Spain
Venue:
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Year:
2009

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Abstract

Least Squares (LS) and its weighted version are standard techniques to estimate the Diffusion Tensor (DT) from Diffusion Weighted Images (DWI). They require to linearize the problem by computing the logarithm of the DWI. For the single-coil Rician noise model it has been shown that this model does not introduce a significant bias, but for multiple array coils and parallel imaging, the noise cannot longer be modeled as Rician. As a result the validity of LS approaches is not assured. An analytical study of noise statistics for a multiple coil system is carried out, together with the Weighted LS formulation and noise analysis for this model. Results show that the bias in the computation of the components of the DT may be comparable to their variance in many cases, stressing the importance of unbiased filtering previous to DT estimation.