Introduction to tomography 0800-WTOMO

The lecture covers the following topics:
1. tomographic methods used in medicine (physical basis, applications):
- computed tomography (CT)
- magnetic resonance tomography (MRI)
- PET
- SPECT
- OCT
2. sources of X-rays
3. interaction of X-rays with matter
4. detection of X-rays
5 Statistics of X-ray photons
6 Lambert-Beer law
Radon transform and its cross sections, sinogram 9.
Fundamentals of Fourier analysis 10.
Fourier cross section theorem 11.
Reconstruction of object cross-section based on set of projections
cross-section reconstruction based on a set of projections in a parallel beam - the role of the filter; discretization of patterns 12.
Cross-section reconstruction using algebraic method 13.
Imaging quality and artifacts in tomographic images

Exercises are designed to provide students with the following skills:
- determining the cross section of the Radon transform of simple objects -.
(homogeneous square, homogeneous triangle, etc.),
- splicing of the discretized cross section of the Radon transform
and filter,
- Determination of solution of system of linear equations using
iterative method.

Total student workload

75 lesson hours (45 min each) including: a) contact hours (lecture and tutorials): 30 h b) individual work: 45 h - 30 hours for current preparation for the consecutive lectures, exercises and tests - 15 hours to prepare for the exam

Learning outcomes - knowledge

W1: knows the principles of construction and physical basis of operation of CT, MRI, PET, SPECT, OCT scanners W2: knows the physical phenomena occurring during interaction of X-rays with matter, in particular with biological tissues W3: understands the essence of algorithms constituting the basis of tomographic reconstruction W4: knows the types of artifacts present in tomographic images and the reasons of their appearance These specific learning outcomes are within the scope of outcomes K_W01 & K_W03

Learning outcomes - skills

U1: can practically determine Radon transforms of simple objects U2: can practically apply elements of tomographic algorithms in case of simple model systems These detailed learning outcomes are within the scope of the K_U05 effect.

Learning outcomes - social competencies

K1: knows the limits of knowledge and skills acquired in the course of study K2: understands the necessity of their self-reliant supplementation These particular educational results are within the scope of the K_K01 effect.

Teaching methods

Lecture - problem lecture, demonstration Exercises - exercise method, classical problem method Expository teaching methods: - demonstration Didactic methods giving: - problem lecture Exploratory didactic methods: - classical problem method

Observation/demonstration teaching methods

- display

Expository teaching methods

- problem-based lecture

Type of course

compulsory course

Prerequisites

Basic knowledge of electromagnetic radiation. Knowledge of basic mathematical analysis (differentiation and integration of functions of one and many variables) and linear algebra (vectors, matrices, systems of linear equations).

Course coordinators

Katarzyna Komar

Assessment criteria

Two written tests will be performed at the end of course:
- a test for passing the tutorials consists of problems to solve on: determining the cross section of the Radon transform, splicing its discretized version with a filter and iterative solution of a simple system of linear equations
- an exam will be open test to check basic knowledge and understanding of the topics discussed in the lecture.

Grading criteria:
50-60% - mark: 3.0
60-70% - mark: 3.5
70-80% - mark: 4.0
80-90% - evaluation: 4.5
90-100% - grade: 5.0

The exam checks the effects of: W1, W2, W3, W4, K1, K2
Colloquium examines effects: U1, U2, K1, K2

Practical placement

not applicable

Bibliography

- T. M. Buzug, Computed tomography (Springer-Verlag Berlin Heidelberg 2010)
- A. C. Kak, M. Slaney, Principles of Computerized Tomographic Imaging, (IEEE Press, New York)
- S. Webb (ed.), The Physics of Optical Imaging, (IOP, Bristol 1996).
- R. F. Farr, P. J. Allisy-Roberts, Physics for Medical Imaging (Saunders, London 1997).

Notes

Term 2022/23L:

Due to the SARS-CoV-2 virus pandemy, lecture and tutorials are conducted remotely via MS Teams.

Passing the tutorials - on the basis of homework tasks assigned during the course and one problem solved by the student during the test on MS Teams.
Passing the lecture - oral exam, remotely, on MS Teams.

The assessment criteria are the same as in the basic information about the course.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 0800-WTOMO in USOSweb