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

Study level:
Advanced studies
Grading scale:
Pass - fail
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2020-2021, 2021-2022, 2022-2023, 2023-2024


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

Learning outcomes

After the course student
  • 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

Description of prerequisites

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

Study materials

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

Completion methods

Method 1

A presentation, a take-home exam and completing an online course. Self-study based on an online material and online exercises. Optional weekly computer classes. In the end of the course a student gives a short presentation and completes a take-home exam.
Evaluation criteria:
For a pass grade a student must complete an online course, a take-home exam and give a presentation.
Select all marked parts
Parts of the completion methods

Participation in teaching (4 cr)

Participation in teaching
Grading scale:
Pass - fail
English, Finnish
No published teaching