MAT-62006 Inverse Problems, 7 cr
Additional information
Suitable for postgraduate studies.
The implementation will not be executed during the academic year 2017-2018.
Person responsible
Sampsa Pursiainen, Mikko Kaasalainen
Lessons
| Implementation | Period | Person responsible | Requirements |
| MAT-62006 2017-01 | - |
Mikko Kaasalainen Sampsa Pursiainen |
Exam + project work/problem classes |
Learning Outcomes
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.
Content
| Content | Core content | Complementary knowledge | Specialist knowledge |
| 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 |
Study material
| Type | Name | Author | ISBN | URL | Additional information | Examination material |
| Lecture slides | Inverse Problems | Fox, Nicholls, Tan | No | |||
| Lecture slides | Inverse Problems | Samuli Siltanen | Yes | |||
| Lecture slides | Käänteiset ongelmat | Jari Kaipio | No | |||
| Summary of lectures | Inverse problems course text | Mikko Kaasalainen | Yes | |||
| Online book | Inversio-ongelmat | Erkki Somersalo | No |
Prerequisites
| Course | Mandatory/Advisable | Description |
| MAT-60000 Matriisilaskenta | Mandatory | |
| MAT-60006 Matrix Algebra | Mandatory |
Correspondence of content
| Course | Corresponds course | Description |
| MAT-62006 Inverse Problems, 7 cr | MAT-52506 Inverse Problems, 6 cr |