COST Training School on Algebraic Reconstruction Methods in Tomography

April 4–6, 2016, Technical University of Denmark.

This training school is part of the EXTREMA COST Action MP1207. It takes place over 3 days at DTU, the Technical University of Denmark, located north of Copenhagen.

Course Description

Algebraic reconstruction methods for computed tomography (CT), such as ART (Kaczmarz's method) and SIRT, provide an interesting alternative to “analytical” methods, such as filtered back projection. They allow more flexibility in the forward model as well as easy incorporation of constraints on the reconstruction – at the expense of longer computing times.

This training school is aimed at participants who are interested in the formulation, implementation, and use of algebraic iterative reconstruction methods. We give a rigorous mathematical description of the reconstruction methods, the associated algebraic models, and the underlying linear algebra, followed by 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 the algebraic methods, and thus be able to use them for their own CT problems.

The participants are expected to be familiar with computed tomography and filtered back projection, with MATLAB, and with basic aspects of linear algebra, and they must bring their own laptop.

The training school is arranged back-to-back with the workshop HD-Tomo Days on modern tomographic imaging methods and numerical solution techniques built on regularization, optimization, and PDE anaysis.

Monday, April 4 – Basic Concepts and Methods (Per Christian Hansen, DTU Compute)

Discretization of the CT problem, leading to linear systems of equations A x = b. Pdf-file with slides.
Linear algebra, solving linear equations, a bit of optimization, and algebraic iterative reconstruction algorithms for CT problems. Pdf-file with slides.
MATLAB hands-on computer exercises using the software package AIR Tools. Pdf-file with exercises.
Program
9:00 - 09:45 Discretization of the CT problem
9:45 - 10:00 Coffee & tea break
10:00 - 11:00 Algebraic methods, part I (slides 1-21)
11:00 - 12:00 Exercises, part I + coffee & tea
12:00 - 13:00 Lunch break
13:00 - 13:45 Algebraic methods, part II (slides 22-35)
13:45 - 14:45 Exercises, part II + coffee & tea
14:45 - 15:30 Algebraic Methods, Part III (slides 36-50)
15:30 - 16:30 Exercises, Part III + coffee & tea

Tuesday, April 5 – Large-Scale Aspects (Willem Jan Palenstijn, CWI Centrum Wiskunde & Informatica)

Block algebraic methods for CT and their performance (Hans Henrik B. Sørensen, DTU Compute).
Computational methods for large-scale CT problems.
The software package ASTRA and its algebraic reconstruction algorithms.
MATLAB hands-on computer exercises using the ASTRA software.
Program
9:00 - 10:00 Block algebraic methods - Slides
10:00 - 10:30 Introduction to ASTRA - Slides intro - Slides usage - Slides topics
10:30 - 12:00 Exercises + coffee & tea Slides exercises
12:00 - 13:00 Lunch break
13:00 - 13:30 Anvanced use of ASTRA
13:30 - 15:15 Exercises + coffee & tea
15:15 - 16:00 ASTRA extra topics
16:00 - 17:00 Hands-on session and discussion

Wednesday, April 6 – State-of-the-Art Imaging Methods (joint with the HD-Tomo Days workshop)

Mini-tutorial: Computational Bayesian Inversion (Klaus Mosegaard, Copenhagen University) Slides
Invited lectures about other state-of-the-art reconstruction paradigms (pdf-file with program).

Participants are encouraged to stay the whole week and seize the opportunity to learn about several different approaches to tomographic reconstruction.

Practical Issues

Meals. Lunch, coffee, tea and refreshments are provided by us. Please indicate any dietary restricions on the registration page.

Travel, accomodation, and reimbursement. Participants must arrange travel and accommodation themselves. For more practical information (the venue, getting to DTU, and suggestions for hotels) please refer to this page for the workshop. Participants of the training school from outside Denmark will be partially reimbursed by COST (more information later).

PCH, Jan. 11, 2016