Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


You will learn to identify an ill-posed inverse problem and to understand the restrictions its nature imposes on the solution process. You will familiarize yourself with several classical regularization methods for finding approximate solutions to linear ill-posed problems. You will learn to formulate an inverse problem as a Bayesian problem of statistical inference and to interpret the information contained in the resulting posterior probability distribution. You will learn to numerically implement the introduced solution techniques.


Credits: 5

Schedule: 01.03.2021 - 09.04.2021

Teacher in charge (valid 01.08.2020-31.07.2022): Nuutti Hyvönen

Teacher in charge (applies in this implementation): Nuutti Hyvönen

Contact information for the course (valid 04.02.2021-21.12.2112):

Lecturer: Nuutti Hyvönen (

Assistant: Juha-Pekka Puska (

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    The course s topic is computational methods for solving inverse problems arising from practical applications. The course consists of two parts: the first three weeks focus on classic regularization techniques, the latter three weeks discuss statistical methods.


  • Applies in this implementation:


Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Teaching methods: lectures, exercises and home exam.

    Assessment methods: exercises, a home exam.


  • Applies in this implementation:

    The students are assumed to participate actively in the course by weekly returning their solutions to one home assignment (typically involving MATLAB computations). 25% of the overall grade is based on the home assignments and 75% on a home exam.

  • Valid 01.08.2020-31.07.2022:

    Contact hours 36h (no compulsory attendance)

    Self-study ca 100h



Study Material
Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:



  • Valid 01.08.2020-31.07.2022:

    MS-A00XX, MS-A01XX, MS-A02XX, MS-A050X. The courses MS-A030X, MS-C134X, MS-C1650, MS-E1460, MS-E1651, MS-E1652, MS-E2112 may also be useful.


Details on the schedule
  • Applies in this implementation:

    • Week 1: Motivation and (truncated) singular value decomposition
    • Week 2: Morozov discrepancy principle and Tikhonov regularization
    • Week 3: Regularization by truncated iterative methods
    • Week 4: Motivation and preliminaries of Bayesian inversion, preliminaries of sampling
    • Week 5: Prior models, Gaussian densities, MCMC (Metropolis-Hastings algorithm)
    • Week 6: MCMC (Gibbs sampler), hypermodels