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Name (Acronym)Inverse Problems (Ill-Posedness and Regularization): Theory, Techniques, and Engineering Applications (IP)
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ECTS4
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Contact E-maildidattica@eledia.org
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LanguageEnglish
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ABSTRACT
Inverse problems (IPs) have been traditionally considered as mathematically challenging because they are intrinsically ill-posed. There are many practical IPs in a variety of engineering disciplines requiring suitable mathematical tools for their robust/stable solution, by recovering the well-posedness typical of forward/direct problems through suitable regularization and information-acquisition/exploitation techniques. Since industry requires fast and simple algorithms for the solution of a wide variety of IPs arising in several engineering fields, this implies a growing need for users that do not have a very high degree of mathematical education. The course will review fundamentals and main issues of IPs, then focusing on classical/state-of-the-art and recently introduced inverse solution procedures and algorithms. Applicative examples including exercises will corroborate the theoretical concepts.COURSE CONTENT
- Introduction and basics: motivations (methodological, applicative), synthesis and design problems in engineering as IPs;
- Formulation of IPs and numerical techniques for dealing with their resolution;
- Ill-posedness and non-linearity: on the role of information in IPs;
- Ill-posedness and the need for regularization;
- Non-linearity: physical meaning, degree of non linearity, the role of a-priori/available information;
- Solution of IPs as minimization/maximization of a cost-function/functional;
- Multi-resolution and information-acquisition strategies as an effective recipe to counteract ill-posedness and non-linearity;
- Applicative examples including exercises regarding specific engineering applications.
TEACHING ACTIVITIES
- Theoretical Lessons
- e-Xam Self Assessment (each teaching class or periodically)
- MATLAB Hands-On
- e-Xam Final Assessment
FURTHER READINGS
- F. D. Moura Neto, A. J. da Silva Neto, “An Introduction to Inverse Problems with Applications”. Springer, 2013.
- A. Tarantola, “Inverse Problem Theory and Methods for Model Parameter Estimation”. SIAM, 2005.
- R. C. Aster, B. Borchers, and C. H. Thurber, “Parameter Estimation and Inverse Problems”. Elsevier, 2013.
- “Microwave Imaging and Diagnostics: Theory, Techniques, and Applications”, European School of Antennas (ESoA) and European Cooperation in Science and Technology (COST Actions TD1301/TU1208), Madonna di Campiglio, Italy, 24-28 March 2014.
- “Microwave Imaging and Diagnostics: Theory, Techniques, and Applications”, European School of Antennas (ESoA), Madonna di Campiglio, Italy, 19-23 March 2018.
- “Microwave Imaging and Diagnostics: Theory, Techniques, and Applications,” European School of Antennas (ESoA), Napoli, Italy, 1-5 February 2021.