1University of Southern California, 90089, CA, United States, 2University of Southern California, Los Angeles, CA, United States
Diffusion MRI can be modeled as sampling the Fourier transform of the
Ensemble Average Propagator (EAP). This is potentially advantageous because of
extensive theory that has been developed to characterize sampling requirements,
accuracy, and stability for Fourier reconstruction. However, previous work has not taken advantage
of this characterization. This work
presents a novel theoretical framework that precisely describes the
relationship between the estimated EAP and the true original EAP. The framework is applicable to arbitrary
linear EAP estimation methods, and for example, provides new insights into the
design of q-space sampling patterns
and the selection of EAP estimation methods.
