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Name (Acronym)Inverse Problems and Imaging (IPI)
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ECTS4
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Contact E-maildidattica@eledia.org
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Teacher
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Syllabus
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Institution
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Study Program
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Degree
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LanguageEnglish
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Tracks
ABSTRACT
Inverse problems (IPs) have been traditionally considered as mathematically challenging because they are intrinsically ill-posed. Imaging problems are a class of IPs with many practical applications in a variety of engineering disciplines, ranging from biomedical diagnostics to industrial non-destructive testing, up to geophysics and security screening, just to mention a few. Such IPs require suitable mathematical tools for their robust/stable solution in order to recover the well-posedness typical of forward/direct problems through suitable regularization and information-acquisition/exploitation techniques. 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, with main emphasis on the techniques for imaging and localization. Applicative examples including exercises will corroborate the theoretical concepts.COURSE CONTENT
- Introduction and basics: motivations (methodological, applicative), imaging problems in engineering as IPs;
- Formulation of IPs and numerical techniques for dealing with their resolution;
- Non-linearity and ill-posedness: on the role of information in IPs;
- Non-linearity: physical meaning, degree of non linearity, the role of a-priori/available information;
- Ill-posedness and the need for regularization;
- 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;
- Numerical techniques for imaging problem solving in biomedical and industrial contexts;
- 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
- M. Bertero and P. Boccacci, “Introduction to Inverse Problems in Imaging”. IoP Press, 1998.
- D. Colton and R. Kress, “Inverse Acoustic and Electromagnetic Scattering Theory”, Springer-Verlag, 1998.
- F. D. Moura Neto, A. J. da Silva Neto, “An Introduction to Inverse Problems with Applications”. Springer, 2013.
- M. Pastorino and A. Randazzo, “Microwave Imaging – Methods and Applications”. Artech House, 2018.
- G. Franceschetti, “Electromagnetics Theory, Techniques, and Engineering Paradigms”, Kluwer Academic/Plenum Publishers, 1997.
- W. C. Chew, “Waves and Fields in Inhomogeneous Media”, Oxford University Press, 1996.