## This website is no longer updated.

As of 1.10.2022, the Faculty of Physics has been merged into the TUM School of Natural Sciences with the website https://www.nat.tum.de/. For more information read Conversion of Websites.

de | en

# Inverse Problems in Medical Imaging

## Module IN2409

This Module is offered by TUM Department of Informatics.

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Basic Information

IN2409 is a semester module in English language at Master’s level which is offered in summer semester.

This Module is included in the following catalogues within the study programs in physics.

• Focus Area Imaging in M.Sc. Biomedical Engineering and Medical Physics
150 h 60 h 5 CP

### Content, Learning Outcome and Preconditions

#### Content

Introduction and examples of inverse problems; vector spaces; definition of inverse problem; well-posedness according to Hadamard; injection, surjection, bijection of functions; Null-space and range space of operators; linear inverse problems; eigenvalue problem; decomposition theorem; singular value decomposition; inverse methods based on length; least squares and determinancy; minimum length; the generalized inverse; nonlinear inverse problems; regularization methods and comparison of different classes; Computed Tomography; Radon transform; backprojection; Fourier-slice theorem; filtered backprojection; deconvolution methods.

#### Learning Outcome

The students will learn basic mathematical tools to analyze and solve inverse problems. The aim of this lecture is to provide sufficient understanding of the underlying inverse problems and strategies for solving these problems. At the end of the lecture, the students will be able to theoretically and practically analyze, experimentally design and implement the required algorithms to solve various inverse problems in medical imaging.

#### Preconditions

Good knowledge of mathematics (Bachelor course)

### Courses, Learning and Teaching Methods and Literature

#### Courses and Schedule

VO 2 Inverse Problems in Medicine Hammernik, K. singular or moved dates
eLearning
UE 2 Inverse Problems in Medicine (IN2409) Hammernik, K. singular or moved dates

#### Learning and Teaching Methods

Interactive Lecture, theoretical and practical Exercises

#### Media

PowerPoint, Whiteboard, interactive Whiteboard (Miro)

#### Literature

R. M. Richardson and G. Zandt. Inverse Problems in Geophysics, 2003. (Lecture Notes)
O. Dössel. Bildgebende Verfahren in der Medizin: Von der Technik zur medizinischen Anwendung, 1999.
G. L. Zeng. Medical Image Reconstruction: A Conceptual Tutorial, 2010.

### Module Exam

#### Description of exams and course work

Lecture: 75 min written examination (70% of the final grade) to see if the students have acquired deep understanding of the provided mathematical tools
Practical: Six assignments sheets with theoretical and practical coding exercises (30% of the final grade)

#### Exam Repetition

The exam may be repeated at the end of the semester.

Top of page