Department of Statistics
Rutgers University, New Brunswick
A review of CT scanning, emission tomography, and functional Magnetic Resonance Imaging (fMRI)
A CT scan reconstructs (via Radon's theorem: the line integrals of a density f in the plane determines f) the electron density, f = f(x,y), of an object from its X-ray attenuation measurements. Finding the electron density of the brain is useful for diagnosing lesions, but it is useless in physiology, where one wants to learn where brain function takes place. Physiology is done with emission tomography where a radionucleide
moves under metabolic action to the active part of the brain, but this technique is too slow (as is standard fMRI) if one wants to study brain function of fast mental processes. After reviewing these older methods, I will review MRI and a new method of fMRI where the Fourier transform of the hydrogen spin density is sampled within a few hundred milliseconds to avoid the confounding due to blood flow refreshing some areas faster than others. The trajectory of the Fourier space sampling is that of the winding up of a ball-of-yarn; the sampling region is a small fraction of Fourier space - the small spatial frequencies. A trade-off of spatial resolution for temporal resolution is then made using prolate spheroidal wavelets which we hope will permit the study of fast mental processes. Experiments conducted at Stanford with ball-of-yarn sampling will be described.
The fMRI work is joint with Cun-Hui Zhang.
A PowerPoint version of this presentation can be found at the following web page: