Optimal Data Acquisition in fMRI Using Prolate Spheroidal Wave Functions

摘要

Functional magnetic resonance imaging (fMRI) is a technique that can be used to noninvasively study mental activity in a persons brain. fMRI has the potential to answer many interesting questions regarding the way the brain functions. Unfortunately, the drawback to fMRI studies, as they are traditionally performed, is that the temporal resolution is too low to effectively answer questions regarding what happens in an active region of the brain immediately following stimulation. Shepp and Zhang (2000) introduced a new method that could potentially lead to a significant increase in temporal resolution. Their method suggests a way to improve the time resolution in fMRI studies by sampling only a fraction of the points needed to recreate a full image. Instead of full image reconstruction, an optimal prolate spheroidal wave function filter is used to obtain a measurement over the total activity in a predefined region in the brain, B, at successive time points. The sampling region and filter are chosen in order to minimize the energy loss over the region of interest (ROI). The region they suggested to sample was chosen heuristically and corresponds to the scaled polar set of B. It was shown to be near optimal through extensive computer searches. In this article the optimal sampling region is found for the case when the ROI is circular or spherical and the sampling size is small. Based on this result, a new heuristic is introduced for other ROOs, which improves upon the results obtained using the polar set of B.