MATS4320 Introduction to Computational X-ray Tomography (4 cr)

Matlab programming, X-ray transform in 2D, generalized Tikhonov regularization, total variation (TV) regularization, optimization methods, filtered back-projection (FBP), Fourier slice theorem, limited angle X-ray tomography

• Understands X-ray tomography as a matrix model and shows how to detect ill-posedness of a tomographic problem
• Understands basic theorems and results on the X-ray transform
• Can solve linear inverse problems using different regularization and optimization methods
• Understands how different regularization methods can be chosen based on a-priori knowledge
• Knows how to write robust Matlab algorithms for X-ray tomographic reconstructions

Introduction to Computational Inverse Problems (or equivalent knowledge), some knowledge of Fourier analysis and ordinary differential equations is helpful but not mandatory

1. The open MOOC-course of the University of Helsinki: Introduction to Computational Tomography (mooc.helsinki.fi).
2. Jennifer Mueller, Samuli Siltanen: Linear and Nonlinear Inverse Problems with Practical Applications, 2012. (A supporting textbook, but not mandatory.)