Lower Bounds for Accuracy of Estimation in Magnetic Resonance High Angular Resolution Diffusion Imaging Data

High angular resonance diffusion imaging (HARDI) is a popular in vivo magnetic resonance brain imaging technique. Clinicians and neuroscientists often use HARDI to understand the fiber geometry inside a human brain. Carmichael and Sakhanenko (Linear Algebra Appl 473:377-403, 2015) (C-S) in their work investigated estimators of the integral curves and their asymptotic distributions under a noisy tensor field model for the imaging signals. Under their model, the present work establishes the minimax lower bound for the asymptotic risk of the integral curve estimators. Additionally, this work generalizes the results of Sakhanenko (Theory Probab Appl 54:168-177, 2012), where minimax lower bounds for the asymptotic risk of the estimators of the integral curves were established under a simple vector model of the imaging signals perturbed by an additive noise.