A Robust Diffusion Tensor Estimation Method for DTI

In diffusion tensor imaging （DTI），diffusion tensor maps are typically calculated from a sequence of diffusion weighted images. However, the diffusion weighted imaging is often influenced by both thermal noise and physiological noise such as artifacts caused by physiological motions. A robust estimation method based on the constrained M-estimator with high breakdown point and high asymptotic efficiency is proposed in this paper for acquiring more accurate DTI diffusion tensor field. First, during preprocessing phase, thermal noise in the diffusion weighted images is removed by implementing dual-tree complex wavelet transform. Then an appropriate regression starting point can be found by random sampling and considering simultaneously the positivity constraint of the diffusion tensor via the Cholesky factorization. Finally, local minimum of the objective function is obtained to achieve constrained M-estimation of the DTI diffusion tensor. Experiments are performed on the synthetic second-order tensor field and the real DTI data set, both corrupted by various levels of outliers. The calculated results show that the proposed method can remove thermal noise and physiological outliers more efficiently compared with the least square regression model and the Geman-McClure M-estimator which are more robust than the standard least square method. Therefore, the proposed method may be particularly useful for the DTI diffusion tensor estimation.