Course Catalog 2012-2013
Basic

Basic Pori International Postgraduate Open University

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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 modified03.04.2012