|SCIENTIFIC DISCIPLINARY SECTOR||MAT/08|
The credits for the course Application of Mathematics to Medicine (AMM, code 42916) are 7. The course is held during the first semester of the 1°, 2° LM years. On request of one student, the lectures and teaching activities will be delivered in English, otherwise in Italian.
AIMS AND CONTENT
The course intends to describe the mathematical modeling of two very important tomographic problems in the medical field: X-ray tomography and microwave tomography. In both cases, the objective of the discussion is twofold: on the one hand, to emphasize how sophisticated mathematical formalisms are indispensable for the understanding of two problems of such great application value; On the other hand, provide students with the numeric tools needed to process the images from these capture modes.
AIMS AND LEARNING OUTCOMES
This course aims to describe the mathematical modeling of three medical imaging problems: the X-ray tomography, the Positron Emission Tomography and the Magnetic Resonance Imaging. The scope of the course is two-fold: on one hand, we want to highlight how sophisticated mathematics is needed for the comprehension of problems with high practical significance; on the other hand, we want to equip the students with the numerical analysis tools required for the processing of the data acquired with these three modalities.
Fondamenti di Calcolo Numerico
Traditional lectures + 1 lab
Part I: X-ray tomography (overview); Radon transform, formulas for the inversion of the Radon transform (as back projection and filtered back projection), issues of uniqueness.
Part II: positron emission tomography (overview); on the two inverse problems related to positron emission tomography: an imaging problem (inversion of the Radon transform) and a compartment alone (Gauss-Newton optimization scheme)
Part III: magnetic resonance imaging (overview); models for data acquisition and magnetic field distortion, Fourier transform, inversion of the Fourier transform from undersampled data.
Professor’s lecture notes
TEACHERS AND EXAM BOARD
Ricevimento: By appointment via email.
Ricevimento: Office hours by appointment via email
MICHELE PIANA (President)
CRISTINA CAMPI (President Substitute)
The class will start according to the academic calendar.
The prerequisites are: Hilbert spaces, continuous linear operators between Hilbert spaces, Fourier analysis