**Mathematics
Department**

**Student:** Vidya
Venkateswaran

**School:** Rutgers University

**Email:** vidyav@dimax.rutgers.edu

**Project Advisor:**
Professor Stanley M.
Dunn

**Project Topic:**
Mathematical Biology

**Project Description:**

**
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.**

**Research Papers:**

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