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Course Catalog 2011-2012
MAT-52506 Inverse Problems, 6 cr |
Additional information
Suitable for postgraduate studies
Person responsible
Mikko Kaasalainen
Lessons
| Study type | P1 | P2 | P3 | P4 | Summer | Implementations | Lecture times and places |
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Requirements
Exam + project work/problem classes
Completion parts must belong to the same implementation
Principles and baselines related to teaching and learning
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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 | Edition, availability, ... | Examination material | Language |
| Lecture slides | Inverse Problems | Fox, Nicholls, Tan | English | ||||
| Lecture slides | Inverse Problems | Samuli Siltanen | English | ||||
| Lecture slides | Käänteiset ongelmat | Jari Kaipio | Suomi | ||||
| Summary of lectures | Inverse problems course text | Mikko Kaasalainen | English | ||||
| Online book | Inversio-ongelmat | Erkki Somersalo | Suomi |
Prerequisite relations (Requires logging in to POP)
Correspondence of content
| Course | Corresponds course | Description |
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More precise information per implementation
| Implementation | Description | Methods of instruction | Implementation |
| Inverse problems: introduction, basic method toolbox, and case studies |