The Department of Mathematics & Statistics would like to welcome:

**Dr. Sarah Hamilton,** on Monday, December 2, at 11:30 am, in SCP 229.

**Title:** Inverse Problems in Medical Imaging: An Introduction to Electrical Impedance Tomography

**Abstract:** Without even realizing it, we are surrounded by inverse problems on a daily basis. In an inverse problem, an observation is your data and you aim to determine what set of circumstances, or conditions, led to that data. For example, if you observe contaminated water in a river at point B, you may aim to determine where, point A, the contamination originates. Inverse problems are particularly abundant in common medical imaging modalities such as: ultrasound imaging, X-ray tomography, MRI, etc., where your data corresponds to some physical measurement and you aim to determine the internal structure that would give rise to said measurements. In this introductory talk, we will explore the key mathematical and computational aspects of various applied inverse problems, in particular for the non-invasive imaging modality Electrical Impedance Tomography (EIT). In EIT, harmless currents are applied on electrodes placed at the surface of a body, and the resulting voltages are measured. From these surface electrical measurements, we aim to recover the internal conductivity of the body and form images that a doctor can use for diagnostic/evaluative purposes. Applications include lung and heart monitoring of ICU patients, breast cancer detection, stroke classification, and brain imaging, just to name a few. We will discuss the most commonly used (linearized) reconstruction approaches, how we can use mathematics to recover a more accurate conductivity, and see how the improved mathematical methods work for real world thoracic imaging!