Course Catalog 2012-2013 Basic Basic Pori International Postgraduate Open University |Degrees|     |Study blocks|     |Courses|

Course Catalog 2012-2013

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
Lectures	24 h/per	+12 h/per				MAT-52506 2012-01

Requirements

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

Principles and baselines related to teaching and learning

-

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
MAT-52506 Inverse Problems, 6 cr	MAT-62006 Inverse Problems, 7 cr
MAT-52506 Inverse Problems, 6 cr	MAT-52500 Inverse Problems, 6 cr

More precise information per implementation

Implementation	Description	Methods of instruction	Implementation
MAT-52506 2012-01	Inverse problems: introduction, basic method toolbox, and case studies

Last modified

03.04.2012