MAT-62007 Inverse Problems, 5 cr
Lisätiedot
Suitable for postgraduate studies.
Vastuuhenkilö
Mikko Kaasalainen
Osaamistavoitteet
Examples of inverse problems include medical imaging (CT, MRI), underground prospecting for ores using electrical measurements, recovering the shape of an asteroid from lightcurve observations, and sharpening a blurred photograph. These problems are sensitive to measurement errors: straightforward inversion attempts lead to failure. Therefore spezialized solution methods are needed. This course gives an overview of classical and modern solution methods for inverse problems. Both theory and computer implementation are discussed, and the methods are demonstrated with practical inverse problems involving measured data.
Sisältö
| Sisältö | Ydinsisältö | Täydentävä tietämys | Erityistietämys |
| 1. | Singular value decomposition of a matrix and solution by SVD truncation. Classical and generalized Tikhonov regularization. | ||
| 2. | Total variation regularization with emphasis on implementation issues. | ||
| 3. | Regularization using truncated iterative solvers. | ||
| 4. | Introduction to statistical (Bayesian) inversion. Theory and implementation of Monte Carlo Markov Chain methods. | ||
| 5. | Practical applications: inverse problems of generalized projections |
Esitietovaatimukset
| Opintojakso | P/S | Selite |
| MAT-60000 Matriisilaskenta | Mandatory | |
| MAT-60006 Matrix Algebra | Mandatory |
Vastaavuudet
Opintojakso ei vastaan mitään toista opintojaksoa