HIDA Course - Regularization in Image Reconstruction: From Model to Data Driven Methods

This repository provides the python notebooks and code snippets for the HIDA course Regularization in Image Reconstruction: From Model to Data Driven Methods. The course and the materials here are provided by

• Samira Kabri,
• Lorenz Kuger,
• Lukas Weigand,
• Tim Roith and
• Martin Burger.

The course is structured in 4 Jupyter notebooks with different topics and an additional setup notebook. We briefly detail the contents below.

Test your Setup: Package10-Setup-Test.ipynb

With this notebook you can check your python environment, such that all the other notebooks can be executed.

Introduction to Inverse Problems: Tutorial_01.ipynb

In this notebook we briefly introduce the world of inverse problems. Most importantly we learn about the radon transformation! Throughout the notebook there are small tasks that challenge your understanding of the material. The solutions are provided in the notebook Tutorial_01_Solutions.ipynb.

Regularization for Inverse Problems: Tutorial_02.ipynb

In this notebook we learn about regularization for inverse problems. We start with the Tikhonov regularization and then move on to total variation and wavelet-based regularization. Again, there are small tasks for which the solutions can be found in Tutorial_02_Solutions.ipynb.

Deep Learning for Inverse Problems: Tutorial_03.ipynb

In this notebook we learn about deep learning for inverse problems. We start with an end-to-end aprroach emplyoing a U-Net. We then introduce the concept of plug-and-play regularization

Sampling in Inverse Problems: Tutorial_04.ipynb

In this notebook introduce the basics of sampling and uncertainty quantification. Again, we apply these insights to CT reconstruction. The solutions to the tasks can be found in Tutorial_04_Solutions.ipynb.