Fast functional MRI

What happens in a persons brain when they see a picture of somebody they recognize? Recognition takes place almost immediately. But where in the brain does it take place? Functional Magnetic Resonance Imaging (fMRI) is a technique which can be used to study mental activity in the brain. However as currently used, the temporal resolution of fMRI studies are too slow to answer such questions. To increase its usefulness, new methods of speeding up fMRI studies must be introduced. In this paper we discuss a method which improves the time resolution in fMRI. Using prior knowledge of the region of interest (ROI) and the time constraints we wish to obtain, the method tailors the k-space (Fourier space) sampling region and creates a matching prolate spheroidal wave function filter in order to maximize the energy concentration in the ROI. The method enables one, at high time resolution, to study the total activity over a pre-defined region of the brain. Thereby giving the opportunity to study the change in mental activity that occurs in that region, when a specific task is performed. This is a problem that, besides having a clear medical interest, also involves interesting mathematical and statistical aspects, especially in Fourier and time series analysis.