MAT-62006 Inverse Problems, 7 cr

Lisätiedot

Suitable for postgraduate studies.

Vastuuhenkilö

Sampsa Pursiainen, Mikko Kaasalainen

Opetus

Toteutuskerta	Periodi	Vastuuhenkilö	Suoritusvaatimukset
MAT-62006 2016-01	4	Mikko Kaasalainen Sampsa Pursiainen	Exam + project work/problem classes

Osaamistavoitteet

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.

Sisältö

Sisältö	Ydinsisältö	Täydentävä tietämys	Erityistietämys
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

Oppimateriaali

Tyyppi	Nimi	Tekijä	ISBN	URL	Lisätiedot	Tenttimateriaali
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

Esitietovaatimukset

Opintojakso	P/S	Selite
MAT-60000 Matriisilaskenta	Mandatory
MAT-60006 Matrix Algebra	Mandatory

Vastaavuudet

Opintojakso	Vastaa opintojaksoa	Selite
MAT-62006 Inverse Problems, 7 cr	MAT-52506 Inverse Problems, 6 cr

Päivittäjä:

Kaasalainen Mikko, 13.10.2016