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

Three modules in the three weeks of January 7-25, 2019, Technical University of Denmark

The course takes place at DTU, the Technical University of Denmark, on the main campus in Lyngby located north of Copenhagen, in room 109, building 308.

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, Algebraic Reconstruction Methods, and 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 partcipants without a stand-alone license we provide access to MATLAB on our servers (you must still bring a laptop).

The course is divied into three stand-alone modules, each of one week, which can be followed independently. Each module will finish with a micro-project on the last day (Friday). A few guest lectures will be sprinkled over the course.

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 the course home page).

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

Practical Details.

We start each day at 9 am and continue to about 4:30 pm, with a lunch break at noon and with a combination of lectures and computer exercises. Meals are NOT provided by us; please use the university canteen.

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. For practical information about the Lyngby DTU campus and getting there please see this page.

Most of the course material for the first two weeks is now up to date.

Module 1: January 7-11 - CT Problems, Filtered Back Projection, SVD Analysis

Per Christian Hansen, Bart van Lith and Nicolai Andre Brogaard Riis, all three from DTU Compute.

Course material:

Our slides contain all the necessary material for the course. For more background material about X-ray CT, the underlying physics, medical applications, etc. we recommend the following books (not provided in this course): Course plan:

Module 2: January 14-18 - Algebraic Iterative Reconstruction Methods

Per Christian Hansen, Bart van Lith and Hans Henrik B. Sørensen, all three from TU Compute.
Willem Jan Palenstijn from the Computational Imaging group at CWI Centrum Wiskunde & Informatica.

Course material:

Course plan:

module 3: January 21-25 - Optimization Methods and Their Use in CT Reconstruction

Martin S. Andersen, Yiqiu Dong, and Alessandro Perelli, everyone at DTU Compute.

Course material:

Course plan: