Course Catalog 2013-2014
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Basic Pori International Postgraduate Open University

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Course Catalog 2013-2014

MAT-62006 Inverse Problems, 7 cr

Additional information

Suitable for postgraduate studies
Will not be lectured year 2013-2014

Person responsible

Mikko Kaasalainen

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         No    English  
Lecture slides   Inverse Problems   Samuli Siltanen         Yes    English  
Lecture slides   Käänteiset ongelmat   Jari Kaipio         No    Suomi  
Summary of lectures   Inverse problems course text   Mikko Kaasalainen         Yes    English  
Online book   Inversio-ongelmat   Erkki Somersalo         No    Suomi  

Prerequisites

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

Prerequisite relations (Requires logging in to POP)



Correspondence of content

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

Last modified24.02.2013