Statistical analysis of a nonlinear estimator for ADC and its application to optimizing diffusion weighting factors

In this paper, we develop a model for estimating the accuracy of a nonlinear estimator used in estimating the apparent diffusivity coefficient (ADC) which provides useful information about the structure of tissue being imaged with diffusion weighted MR. Further, we study the statistical properties of the nonlinear estimator and use them to design optimal diffusion weighting factors. Specifically, we show that a weighted linear estimator can well approximate the nonlinear estimator and thus can be used to analyze the statistical properties of the nonlinear estimator. Furthermore, to account for the fact that the ground truth of the ADC is a distribution instead of a single value, a weighted coefficient of variance (COV) is proposed as a criteria to be minimized for the determination of the optimal diffusion weighting factors. Both synthetic and real experiments are shown to depict the performance of our approach.