MS-E1654 - Computational inverse problems, 25.02.2019-05.04.2019
Kurssiasetusten perusteella kurssi on päättynyt 05.04.2019 Etsi kursseja: MS-E1654
Osion kuvaus
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The preliminary versions of the lecture slides can be found below. The slides may still be updated during the course.
Recommended supplementary reading: J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2005 (mainly Chapters 2 and 3), and D. Calvetti and E. Somersalo, Introduction to Bayesian Scientific Computing. Ten Lectures on Subjective Computing, Springer, 2007.
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Fedruary 25
Practical issues, motivation, compact operators and singular value decomposition, Fredholm equation and its solvability.
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March 1
Truncated singular value decomposition, pseudoinverse.
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March 4
Morozov discrepancy principle, Tikhonov regularisation and its generalizations.
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March 8
Regularization by truncated iterative methods: Landweber-Fridman iteration.
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March 11
Regularization by truncated iterative methods: conjugate gradient method.
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March 15
Conjugate gradient method (cont.), preliminaries of statistical inversion.
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March 18
Preliminaries of statistical inversion (cont.), construction of likelihood.
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March 22
Construction of likelihood (cont.), sampling, prior models.
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March 25
Prior models (cont.), n-variate Gaussian densities.
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March 29
Improper Gaussian priors, MCMC: Metropolis-Hastings algorithm.
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April 1
Gibbs sampler, judging the quality of a sample.
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April 5
Hyper models.
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