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 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.

Conditioning

Tomography

Scattering

Inversion

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 ultrassonography in terms of acoustic wave propagation in inhomogeneous mediums;

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

- 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 ultrassonography in terms of acoustic wave propagation in inhomogeneous mediums;

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

1) Inverse Problems

2) Mathematical Models for Computarized Tomography

3) Mathematical Models for Ultrassonography

2) Mathematical Models for Computarized Tomography

3) Mathematical Models for Ultrassonography

• 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;

• 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.