Course Catalog 2008-2009
Basic

Basic Pori International Postgraduate Open University

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Course Catalog 2008-2009

MAT-52506 Inverse Problems, 6 cr

Course´s person responsible

Samuli Siltanen

Implementations

  Lecture times and places Target group recommended to
Implementation 1


Per 1 :
Tuesday 10 - 11, TB110

 
3.-n. vuosikurssi
Biotekniikan koulutusohjelma
DI-Opiskelijat
Jatko-opiskelijat
Luonnontieteiden ja ympäristötekniikan tiedekunta
Sähkötekniikan koulutusohjelma
Teknis-luonnontieteellinen koulutusohjelma
Tietotekniikan koulutusohjelma  


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

-

Objectives

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

Course O/R
MAT-31096 Matrix Algebra 1 Recommended  

Prerequisite relations (Requires logging in to POP)

Correspondence of content

Course Corresponds course  Description 
MAT-52506 Inverse Problems, 6 cr MAT-52500 Inverse Problems, 6 cr  

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 modified11.08.2008
ModifierSamuli Siltanen