MAT-62006 Inverse Problems, 7 cr

Additional information

Suitable for postgraduate studies
Will not be lectured year 2015-2016

Person responsible

Mikko Kaasalainen

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Requirements

Exam + project work/problem classes
Completion parts must belong to the same implementation

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

Last modified 23.03.2015

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

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

Course	Mandatory/Advisable	Description
MAT-60000 Matriisilaskenta	Mandatory
MAT-60006 Matrix Algebra	Mandatory

Course	Corresponds course	Description
MAT-62006 Inverse Problems, 7 cr	MAT-52506 Inverse Problems, 6 cr