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.

RECOMMENDED READING/BIBLIOGRAPHY

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