Student: Vidya Venkateswaran
School: Rutgers University
Project Advisor: Professor Stanley M. Dunn
Project Topic: Mathematical Biology
My project primarily deals with the mathematical aspects of medical imaging. Ultimately, we would like to determine the image of a various part of the body (example: the brain) This is done by taking finitely many projections of the image typically using X-rays, microwaves, or ultrasound. The projections are specified by an angle and measure the X-ray radiation absorbed. With this data, we then need a mathematical algorithm to "reconstruct" the actual image. Much headway has been made in this area over the decades leading to the widespread use of Fourier analysis to produce viable reconstruction algorithms.
In this project, we investigate algorithms to use when the geometry of the projection is not exactly known. We are studying geometric algebra or "Clifford algebra" to use in conjunction with Fourier analysis. Our goal is to find a more general way to model the location of the dectectors and sources, rather than using Euclidean geometry which fails for complicated setups. We hope to model the geometry using this new type of algebra, and then express a reconstruction algorithm to produce the original image.