Inverse Problems: Summer school

Published
31.7.2024

Courses on inverse problems in JSS34.

General information

qrcode for JSS inverse problems courses

IP1: Mathematics of X-ray Computed Tomography

  • Time: 1-3 pm every day
  • Lecturer(s): Dr. Tatiana Bubba (University of Ferrara, Italy), email: tatiana.bubba@unife.it
  • Code: MATJ5124
  • Modes of study: Lectures + exercises
  • Credits: 2 ECTS
  • Evaluation: Exercises pass/fail
  • Completion: Return exercises to the lecturer, deadline 29th of August
  • Contents: In this course we learn about the mathematics of X-ray computed tomography, what is the regularization theory of inverse problems, and how some signal processing ideas are relevant in the context of inverse problems.
  • Learning outcomes: Basics of X-ray tomography, regularization theory and signal processing
  • Prerequisites: Basics of linear algebra, numerical and functional analysis
  • Material: Slides and exercises here

IP2: Introduction to Uncertainty Quantification for Inverse Problems

  • Time: 9-11 am every day
  • Lecturer(s): Dr. Babak Maboudi (University of Oulu, Finland), email: babak.maboudi@oulu.fi
  • Code: MATJ5125
  • Modes of study: Lectures + exercises
  • Credits: 2 ECTS
  • Evaluation: Exercises pass/fail
  • Completion: Return exercises to the lecturer, deadline 29th of August
  • Contents: In this course, we will explore how to formulate inverse problems within a Bayesian framework. This involves representing both noise and unknowns using probability distributions. We will then define the solution to the inverse problem as the conditional probability distribution of the unknown given the measurements, commonly known as the posterior distribution. Finally, we will examine how to interpret the posterior to quantify the uncertainty in our predictions and reconstructions.
  • Learning outcomes: Formulate an inverse problem with additive noise using a Bayesian framework.
    • Identify appropriate prior distributions based on the problem context.
    • Perform point estimation using maximum a posteriori (MAP) and conditional mean estimates.
    • Implement the Metropolis-Hastings algorithm to explore the posterior distribution.
    • Conduct uncertainty quantification to assess prediction reliability.
  • Prerequisites: Basics of numerical and computational skills, coding in Python is mandatory; Basic knowledge of probability theory and statistics.
  • Course material & Exercises: Github


     

Previous courses

Below are listed the courses in inverse problems for Jyväskylä Summer School for previous years.