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

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

## Description

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 (mooc.helsinki.fi).
2. Jennifer Mueller, Samuli Siltanen: Linear and Nonlinear Inverse Problems with Practical Applications, 2012. (A supporting textbook, but not mandatory.)

## Completion methods

### Method 1

Description:
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
x

### Participation in teaching (4 cr)

Type:
Participation in teaching