Course Catalog 2009-2010 International Basic Pori International Postgraduate Open University |Degrees|     |Study blocks|     |Courses|

Person responsible

Mikko Kaasalainen

Implementations

	Lecture times and places	Target group recommended to
Implementation 1	Per 1 : Monday 10 - 12, TB219 Per 1, 2 : Friday 12 - 14, TB219

Requirements

Passed exam, sufficient activity in exercises, accepted project work.
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 to medical imaging and signal processing. Emphasis on realistic large-scale problems.

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
Online book	Inversio-ongelmat	Erkki Somersalo					Suomi

Prerequisites

Correspondence of content

More precise information per implementation

	Description	Methods of instruction	Implementation
Implementation 1	Teaching in Period 1 consists of lectures and computer exercises. In period 2 the students complete a Matlab project work in small groups (1-3 persons).	Lectures Excercises Practical works	Contact teaching: 0 % Distance learning: 0 % Self-directed learning: 0 %

Last modified	09.09.2009
Modifier	Timo Hämäläinen