802676S Introduction to Inverse Problems (5 op)
Kuvaus
Theory of ill-posed inverse problems, singular value decomposition, Generalized-Inverse and Normal equations, Landweber iterations and Tikhonov regularization, Morozov discrepancy principle. Examples includeconvolutions, Fourier and Radon transform, corresponding to applications in image processing, X-ray and Magnetic Resonance Tomography. Use of Matlab/Python for implementation.
Osaamistavoitteet
After successful completion of the course the student can identify linear ill-posed inverse problems and their severity. Furthermore, the students will be able to analyze and solve such problems with direct and indirect solution methods, identify necessary regularization, is able to implement such methods and work with basic simulated and experimental data.
Lisätietoja
Opetuskieli Englanti Ajoitus 3rd/last year during B.Sc. studies, 1st or 2nd year of Master, 3rd period. Kohderyhmä Students having mathematics, applied mathematics, or statistics as the major or a minor subject.
Esitietojen kuvaus
Esitietovaatimukset Core courses in the B.Sc curriculum of mathematical sciences, especially linear algebra; Numerical Analysis, Fourier analysis (beneficial,but not necessary), Functional analysis (beneficial, but not necessary).