MS-E1654 - Computational inverse problems, 24.02.2020-03.04.2020

Materials

• Materials
  

  Materials

  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.

  • February 24

    Practical issues, motivation, compact operators and singular value decomposition, Fredholm equation and its solvability. 

    • Lecture 1
      • lecture1.pdf129.3KB

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  • February 28

    Truncated singular value decomposition, pseudoinverse.

    • Lecture 2
      • lecture2.pdf123.5KB

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  • March 2

    Morozov discrepancy principle, Tikhonov regularisation and its generalizations.

    • Lecture 3
      • lecture3.pdf128.8KB

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  • March 6

    Regularization by truncated iterative methods: Landweber-Fridman iteration.

    • Lecture 4
      • lecture4.pdf132.2KB

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  • March 9

    Regularization by truncated iterative methods: conjugate gradient method.
    

    • Lecture 5
      • lecture5.pdf227.8KB

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  • March 13

    Conjugate gradient method (cont.), preliminaries of statistical inversion.
    

    • Lecture 6
      • lecture6.pdf148.6KB

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  • March 16

    Preliminaries of statistical inversion (cont.), construction of likelihood.
    

    • Lecture 7
      • lecture7.pdf170.2KB

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  • March 20

    Construction of likelihood (cont.), sampling, prior models.
    

    https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=a707f988-7413-4f57-b107-ab8300b9da62
    
    

    • Lecture 8
      • lecture8.pdf195.6KB

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  • March 23

    Prior models (cont.), n-variate Gaussian densities.

    https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=91ab0e86-3047-4d5b-b4d8-ab84008885f2
    

    • Lecture 9
      • lecture9.pdf130.9KB

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  • March 27

    Improper Gaussian priors, MCMC: Metropolis-Hastings algorithm.

    https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=fcda6f1d-f094-4294-9fd5-ab8400c44951
    

    • Lecture 10
      • lecture10.pdf209.1KB

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  • March 30

    Gibbs sampler, judging the quality of a sample.

    https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=e0aad711-bdad-4e33-a030-ab8800c47b25
    

    • Lecture 11
      • lecture11.pdf1.2MB

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  • April 3

    Hyper models.

    https://aalto.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=75430a96-aa39-4f50-b812-ab9100a53ebd
    

    • Lecture 12
      • lecture12.pdf129.5KB

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