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## APPLICATIONS OF MATHEMATICS TO ASTROPHYSICS

CODE 62425 2021/2022 5 cfu during the 2nd year of 9011 MATEMATICA(LM-40) - GENOVA 5 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA 6 cfu during the 1st year of 9011 MATEMATICA(LM-40) - GENOVA MAT/08 Italian (English on demand) GENOVA 1° Semester AULAWEB

## OVERVIEW

Language: Italian

This course consists of 35 hours of lectures. Moreover, 15 laboratory hours have been planned. According to policy actions needed to get control of the COVID-19 pandemic, part of the lessons will be held in e-learning mode.

## AIMS AND CONTENT

### LEARNING OUTCOMES

The course objective is to provide specialized mathematical training on the proper methods of reconstruction and image processing with particular reference to the processing of astronomical images.

### AIMS AND LEARNING OUTCOMES

The aim of this course is to provide students with basic and advanced mathematical methods for a theoretical analysis and practical solutions of problems in image reconstruction and image processing with specific applications in astronomical imaging. To this aim data from the most recent NASA and ESA missions will be at disposal.

### PREREQUISITES

Each topic will be addressed in a self-consistent way

### TEACHING METHODS

According to policy actions needed to get control of the COVID-19 pandemic, part of the lessons will be held in e-learning mode.

### SYLLABUS/CONTENT

Basics of image processing: 1) Digital images: sampling and quantization. 2) Image formation and image recording: blurring and noise. 3) Point Spread Function. 4) Imaging systems in the frequency domain. Transfer function. 5) Filtering in the frequency domain.

Astronomical image processing:

1. Image reconstruction from visibilities: definition of visibility; inverse Fourier Transform from limited data; deconvolution techniques; iterative methods for image reconstruction. The ESA STIX instrument in Solar Orbiter.
2. Image desaturazione: data formation process in the NASA SDO/AIA instrument; primary saturation, blooming, diffraction fringes; inverse diffraction; mosaicing.
3. Forecasting: feature extraction from SDO/HMI images; neural networks; single layer and multi-layer perceptrons.

1. Bertero M and Boccacci P 1998 An Introduction to Linear Inverse Problems in Imaging (IOP, Bristol)
2. R.C. Gonzalez and R.E. Woods. Digital Image Processing 2nd edition. Prentice-Hall. 200
3. S. Giordano, N. Pinamonti, M. Piana, and A.M. Massone. The process of data formation for the Spectrometer/Telescope for Imaging X-rays (STIX) in Solar Orbiter. SIAM Journal on Imaging Sciences Vol. 8, No. 2, pp. 1315–1331, 2015
4. G. Torre, R.A. Schwartz, F. Benvenuto, A. M. Massone, and M. Piana. Inverse diffraction for the Atmospheric Imaging Assembly in the Solar Dynamics Observatory

## TEACHERS AND EXAM BOARD

### Exam Board

Anna Maria MASSONE (President)

FEDERICO BENVENUTO

MICHELE PIANA (President Substitute)

## LESSONS

### LESSONS START

Lessons will start according to the academic calendar.

### Class schedule

APPLICATIONS OF MATHEMATICS TO ASTROPHYSICS

## EXAMS

Oral.

### ASSESSMENT METHODS

Oral exam (the admission to the oral exam is subject to the approval of the practical exercises during the semester)