Robust Diffusion Tensor Estimation by Maximizing Rician Likelihood

Introduction: Diffusion tensor imaging (DTI) is widely used to characterize white matter in health and disease. Previous approaches to the estimation of diffusion tensors have either been statistically suboptimal or have used Gaussian approximations of the underlying noise structure, which is Rician in reality. The most prevalent tensor estimation method, the log-linear minimum mean squared error (LLMMSE) approach [1], assumes independently, log-Gaussian noise. Sijbers et al. [2] presented an ML approach for Rician bias compensation of single MR images, and Koay et al. [3] demonstrated an exact solution and extended the method for images from multiple coils. Jones et al. [4] presented an estimation method that incorporates noise level estimation. Salvador et al. [5] reviewed distribution assumptions and described a weighted least squares procedure for addressing non-Gaussianity. These methods do not take into account either (1) the propagation of Rician noise into the tensor domain or (2) the dependence between observed attenuations caused by the use of common reference scans. These systematic differences can cause quantities derived from these tensors — e.g., fractional anisotropy and apparent diffusion coefficient — to diverge from their true values, potentially leading to artifactual changes that confound clinically significant ones. Recent developments with Diffusion Tensor Estimation by Maximizing Rician Likelihood (DTEMRL) showed that tensor estimation can be performed by considering the joint distribution of all observed data in the context of an augmented tensor model that accounts for Rician noise [6]. This abstract presents a robust extension of DTEMRL (rDTEMRL) designed to improve reliability in low SNR and artifact prone applications.