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IMAGING PHYSICS SEMINAR

**Debra McGivney**

**Research Scientist, Department of Radiology**

**Case Western Reserve University**

**Inverse Problems in Medical Imaging**

Mathematical inverse problems are used to model a wide variety of practical problems, including problems in medical imaging. Here, the unknown of interest is an image of the inside of the human body, which is not directly observable, but must be reconstructed given measurements made outside of the body. Oftentimes, reconstruction problems in imaging are ill-posed, which can result in errors in the reconstructed solution. Medical imaging plays a vital role in the diagnosis, differentiation, and treatment of various diseases; therefore, it requires that the reconstructed images accurately depict reality.

In this talk, I will describe the concept of mathematical inverse problems and techniques that are used to solve them. Two imaging examples and their associated inverse problems will be considered. First, electrical impedance tomography (EIT), which is a modality that reconstructs the electrical conductivity distribution inside of a body, given voltage measurements made on a set of electrodes attached to the surface. Next, magnetic resonance fingerprinting (MRF) will be discussed, which is a rapid quantitative technique in magnetic resonance imaging (MRI). Partial volume, which occurs when two or more tissue types are present within the spatial limits of a voxel, is an ill-posed inverse problem present in many imaging modalities. We will discuss in detail how to solve this partial volume problem in the MRF framework.

Host: Michael Martens