MAT-62006 Inverse Problems, 7 cr

Additional information

Suitable for postgraduate studies.

Person responsible

Sampsa Pursiainen, Mikko Kaasalainen

Lessons

Implementation Period Person responsible Requirements
MAT-62006 2016-01 4 Mikko Kaasalainen
Sampsa Pursiainen
Exam + project work/problem classes

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 Additional information Examination material
Lecture slides   Inverse Problems   Fox, Nicholls, Tan         No   
Lecture slides   Inverse Problems   Samuli Siltanen         Yes   
Lecture slides   Käänteiset ongelmat   Jari Kaipio         No   
Summary of lectures   Inverse problems course text   Mikko Kaasalainen         Yes   
Online book   Inversio-ongelmat   Erkki Somersalo         No   

Prerequisites

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



Correspondence of content

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

Updated by: Kaasalainen Mikko, 13.10.2016