Mathematics and Applications Seminar 
11:00am - 12:00pm, Friday, Mar 24, 2023 
MSB 318 

Speaker: 
Dr. Alexander Katsevich 
Department of Mathematics 
University of Central Florida

Title: Tomographic Reconstruction - resolution and aliasing 

Abstract:
We will begin by briefly describing the physical principles of computer tomography (CT) and illustrate some of its applications. In the second part of the talk we will overview our recent results on the analysis of resolution of CT reconstruction from discrete Radon transform data, including reconstruction of objects with rough edges. The proposed approach is more powerful than the sampling theory, since it is more flexible and does not require that the function to be reconstructed be band-limited. In the third part we will discuss our latest results on the analysis of aliasing. We consider the generalized Radon transform R in the plane. Let f be a piecewise smooth function, which has a jump across a smooth, convex curve S. We obtain a precise, quantitative formula describing view aliasing artifacts when f is reconstructed from the data Rf discretized in the view direction. The formula is asymptotic, it is established in the limit as the sampling rate goes to zero. Numerical experiments with the classical Radon transform and generalized Radon transform (which integrates over circles) demonstrate the accuracy of the formula. Most of the talk is accessible to graduate and advanced undergraduate students.

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The UCF Mathematics and Applications Seminar, which takes place every Friday from 11am to 12pm in MSB 318, provides a venue for researchers to present their current work, foster new collaborations, and showcase both foundational mathematics and its applications to graduate and undergraduate students.

https://sciences.ucf.edu/math/seminar/mathematics-and-applications-seminar