PT|EN
Problemas Inversos e Imagiologia Médica
Courses Doutoramento em Matemática Aplicada e Modelação
Cod: 23036
Department: DCET
ECTS: 10
Scientific area: Mathematics
Total working hours: 260
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.


 

1) Inverse Problems
2) Mathematical Models for Computarized Tomography and its numerical solution;
3) Mathematical Models for Inverse Obstacle Scaterring Problems and its numerical solution;


 

  • Serranho, Inverse problems and medical imaging: lecture notes, http://hdl.handle.net/10400.2/13335, 2025;
  • Colton, Kress: Inverse Acoustic and Electromagnetic Scattering, Springer, 2012;
  • Natterer, The Mathematics of Computerized Tomography, SIAM, 2001;
  • Natterer, Wuebbling: Mathematical Methods in Image Reconstruction, SIAM, 2001;

 

E-learning

Evaluation is made on individual basis and it involves the coexistence of two modes: continuous assessment (60%) and final evaluation (40%). Further information is detailed in the Learning Agreement of the course unit.