Fast estimation of diffusion tensors under Rician noise by the EM algorithm

Area of Science:

• Neuroimaging
• Biophysics
• Computational Biology

Background:

• Diffusion Tensor Imaging (DTI) is crucial for in vivo characterization of central nervous system white matter.
• Water molecule displacement data in brain tissue is acquired via magnetic resonance scanning.
• Rician noise corrupts magnitude data after Fourier inversion, complicating diffusion estimation.

Purpose of the Study:

• To present a fast computational method for Maximum Likelihood Estimation (MLE) of diffusivities under the Rician noise model.
• To improve the accuracy and precision of diffusion tensor parameter estimation in DTI.
• To extend the MLE framework to Maximum A Posteriori (MAP) estimation.

Main Methods:

• Utilized the Expectation-Maximization (EM) algorithm for MLE under Rician noise.
• Employed data augmentation to convert the non-linear regression problem into a generalized linear model.
• Applied the Fisher-scoring method for rapid convergence of tensor parameters.

Main Results:

• The novel method demonstrated higher accuracy and precision in Rician noise estimation compared to log-normal based methods.
• The approach was validated using both synthetic and real DTI data across a wide range of b-amplitudes (up to 14,000s/mm²).
• Numerical proximity between MLE and MAP estimators was investigated.

Conclusions:

• The developed EM-based MLE method offers a computationally efficient and accurate approach for DTI analysis.
• The findings suggest improved white matter characterization in the human brain.
• The extension to MAP estimation provides further avenues for robust DTI parameter estimation.