PhD Course and Training School:
Scientific Computing for X-Ray Computed Tomography (CT)

Three modules in three weeks of January 2-20, 2023.

All lectures and exercises take place on DTU, Lyngby campus, in building 308 room 109.
It is not possible to participate online.

Course Description

X-Ray Computed Tomography (CT) is a well-known technology that is used routinely in medicine, materials science and many other applications. We probe an object with X-rays and record the response from the object; then using a mathematical model for the interaction between the X-rays and the object, we can reconstruct the object's interior using sophisticated mathematical methods and numerical algorithms.

This training school is aimed at participants who are interested in the formulation, implementation, and use of standard reconstruction methods for CT such as Filtered Back Projection and Algebraic Reconstruction Methods, as well as more novel methods such as Total Variation. We give a rigorous mathematical description of the CT reconstruction problem, the associated mathematical formulations, and the underlying computational algorithms - supplemented with hands-on MATLAB® computer exercises that illustrate these methods. The goal is that the participants will get a basic understanding of the formulation, implementation, and use of basic CT reconstruction algorithms, and thus be able to use them to perform data analysis for their own CT problems.

The participants are expected to be familiar with MATLAB and with basic aspects of linear algebra and optimization, and they must bring their own laptop, preferably with MATLAB. For participants without a license we provide access to MATLAB on our servers (you must still bring a laptop).

The course is divided into three stand-alone modules, each of one week, which can be followed independently. Each module will finish with presentation of a micro-project on the last day (Friday); there will be time every day to work on the micro-project.

Participation in the Course

Students and PhD students from DTU must follow this course over all three weeks as the DTU-course 02946 (link to DTU's course description).

Other participants register for the course by sending a mail to professor Per Christian Hansen indicating which week(s) you wish to attend. There is no course fee.

Practical Details.

All lectures and exercises take place in building 308, room 109 on DTU Lyngby Campus. There is a lot of construction work going on, so make sure that you check the map of the campus. Here is information about getting to DTU Lyngby Campus.

We start each day at 9 am and continue to about 4:30 pm, with several breaks each day. Requirements for passing the course are active participation in the daily exercises and micro-projects and a short oral presentation each Friday afternoon (by the group) of the micro-projects.

Participants must arrange travel and accommodation themselves.

The course material consists of our slides and exercises, which are uploaded here. As supplementary course material we recommend the book P. C. Hansen, J. S. Jørgnsen, and W. R. B. Lionheart (Eds.), Computed Tomography: Algorithms, Insight, and Just Enough Theory, SIAM, Philadelphia, 2021, Fundamentals of Algorithms FA18. Buying the book is not required.

For many of the exercises you will need MATLAB's Image Processing Toolbox, as well as our software package AIR Tools II. You will also need a few m-files available here: Moreover, you will need access to a python compiler and the open-source Core Imaging Library (CIL) software package.

For more background material about X-ray CT, the underlying physics, medical applications, etc. we recommend the following books):

Module 1 (Jan. 2-6): CT Problems, Filtered Back Projection, SVD Analysis

Per Christian Hansen and Jakob Sauer Jørgensen, both from DTU Compute.

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Module 2 (Jan. 9-13): Algebraic Iterative Reconstruction Methods

Per Christian Hansen and Jakob Sauer Jørgensen, both from DTU Compute.

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Module 3 (Jan. 16-20): Optimization Methods and Their Use in CT Reconstruction

Martin S. Andersen and Yiqiu Dong, both from DTU Compute.

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