OVERVIEW

The aim of this module 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. The first part of the module is dedicated to general notions and main operators for image processing. We will therefore address an image reconstruction problem within the Solar Orbiter (ESA) mission, an image processing problem within the SDO/AIA mission (NASA) and a prediction problem within the SDO/HMI mission (NASA). A hands-on laboratory session in MATLAB environment is foreseen for each of the problems addressed. Both the theoretical lessons and the lab sessions will take place in person.

AIMS AND CONTENT

LEARNING OUTCOMES

The course aims to provide specialised mathematical skills on image reconstruction and processing techniques with particular focus on astronomical imaging. To this end, along with theoretical lectures, computer exercises are planned during which real data recorded by currently operational NASA and ESA satellites will be processed.

AIMS AND LEARNING OUTCOMES

Attendance and active participation in the proposed learning activities (lectures and laboratory sessions), along with individual study, will enable students to acquire advanced skills aimed at:

• Handling various types of real astronomical data

• Reconstructing, processing, and inferring information from astronomical images. In particular:

  • Reconstructing X-ray images through Fourier Transform inversion from limited data
  • Desaturating EUV images by solving inverse diffraction problems
  • Solving solar flares forecasting problems by using machine learning techniques

PREREQUISITES

All topics covered in the course are presented in a self-contained manner. However, students are expected to have acquired, during their undergraduate studies, basic knowledge of Numerical Analysis, which is necessary to tackle the subjects of the course. The course Fourier Analysis is recommended

TEACHING METHODS

The course includes theoretical lectures, totaling 32 hours, and three laboratory sessions, totaling 20 hours. Both the lectures and the lab sessions will take place in person. Attendance at the laboratory sessions is highly recommended. At the beginning of each lab activity, a brief theoretical introduction will be given to review the computational techniques to be used and outline the steps to follow. During the practical part, students—working in groups of two or three and supported by the instructors—will be required to implement the described techniques. At the end of each lab session, students must submit their code along with a brief report detailing the methods used and the results obtained. The organization and schedule of the individual lab sessions will be communicated directly by the instructors during the lectures.

SYLLABUS/CONTENT

Basics of image processing: 1) Digital images: sampling and quantization. 2) Basic operators for image processing. 3) Image formation and image recording: blurring and noise. 4) Point Spread Function. 5) Imaging systems in the frequency domain. Transfer function. 6) 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; LASSO regression.

RECOMMENDED READING/BIBLIOGRAPHY

All slides used during the lectures, as well as other teaching materials, will be available on Aulaweb. In general, the notes taken during the lectures and the materials provided on Aulaweb are sufficient for exam preparation. The books and articles listed below are recommended for further reading:

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
5. S. Guastavino and F. Benvenuto. A mathematical model for image saturation with an application to the restoration of solar images via adaptive sparse deconvolution. Inverse problems vol. 37 issue 1 p 15010. 2020

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

In accordance with the academic calendar approved by the Consiglio di Corso di Studi.

Class schedule

APPLICATIONS OF MATHEMATICS TO ASTROPHYSICS

EXAMS

EXAM DESCRIPTION

During the semester, three laboratory sessions will be held, each with a set deadline for the submission of the corresponding code, including a brief report on the methodologies used and the results obtained. A positive evaluation of the lab work is a prerequisite for admission to the final oral exam. For students who have attended at least 75% of the lab hours, the oral exam will focus on the theoretical topics covered in the course. For all others, it will also include more technical aspects of the lab exercises.

Students with disabilities or specific learning disorders (SLD) are reminded that, in order to request accommodations for exams, they must follow the instructions detailed on the following page: https://unige.it/disabilita-dsa/studenti-disturbi-specifici-apprendimento-dsa. In particular, requests for accommodations must be made well in advance (at least 7 days before the exam date) by contacting the instructor and copying both the School's designated contact person and the relevant office (see instructions).

ASSESSMENT METHODS

The laboratory assessments are aimed at testing the practical skills acquired for the solution of the posed problems. They will be evaluated on the basis of the following criteria:

• accuracy and optimization of the code
• accuracy and presentation of the results (images, graphs, tables ...)
• comments on the procedures followed and on the results obtained

The oral exam is finally aimed at assessing the ability to communicate the knowledge acquired in a clear and competent manner

FURTHER INFORMATION

Students with DSA certification (specific learning disabilities), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.