Inverse Problems and Medical Imaging

Inverse Problems and Medical Imaging

Cod: 23036

Department: DCET

Department: DCET

ECTS: 10

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 260

Total contact time: 10

Total contact time: 10

This learning unit (LU) will allow the student to gather knowledge and fundamental skills to the mathematical modeling of inverse problems related with medical imaging, as well as to explore some numerical methods to solve them., including theoretical analysis of the methods and computational implementation.

Since it is a LU with a strong numerical analysis component, the student should have some background in linear algebra, mathematical and numerical analysis and programming.

Most of the supporting study materials are in english.

Conditioning

Tomography

Scattering

Inversion

- Recognize an inverse problem and its difficulties;

- Identify the mathematical modeling of medical image acquisitions as an inverse problem;- Recognize the mathematical model of Computerized tomography in terms of the Radon transform;

- Recognize the mathematical model of acoustic wave propagation and obstacle scattering;

- Identify and apply numerical methods to solve the previous problems.

2) Mathematical Models for Computarized Tomography and its numerical solution;

3) Mathematical Models for Inverse Obstacle Scaterring Problems and its numerical solution;

• Natterer; The Mathematics of Computerized Tomography, SIAM, 2001;

• Natterer, Wuebbling: Mathematical Methods in Image Reconstruction, SIAM, 2001;

E-learning