organized in cooperation with Helmholtz Information & Data Science Academy (HIDA) and Helmholtz Imaging
Regularization in Image Reconstruction: From Model to Data Driven Methods
This 7-hours course covers typical mathematical tasks and caveats of image reconstruction problems. We introduce the theoretical framework of inverse problems and how different imaging modalities and measurement errors can lead to unfavorable reconstructions. Furthermore, we consider regularization strategies to overcome these issues, both from the theoretical and practical side. This fundamental knowledge is to be used as a starting point for self-guided learning during and beyond the course time. Basing off of the classical regularization approaches, the course further gives an introduction into deep learning for inverse problems. Finally, we also explore the Bayesian viewpoint, where we also consider the problem of uncertainty quantification.
The workshop covers a lecture and a tutorial part with hands-on, during which the instructors are available for instructions, feedback and advice.
Learning Goals
Lecture (1h):
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Understand mathematical tasks and caveats of inverse problems, with a special focus on image reconstruction problems.
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Recognize classical regularization approaches and their most relevant mathematical properties.
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Understand the key concepts and pitfalls of learning for inverse problems.
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Realize the importance of uncertainty quantification and the probabilistic/Bayesian approach to inverse problems.
Tutorial part 1 (1h): Introduction to Inverse Problems
In the first part of the tutorial, we briefly introduce the world of inverse problems. With the help of small code examples we explore the practical implications of ill-posedness. Using existing implementations, we also learn about the radon transform and how we can use it in Python.
Tutorial part 2 (1h): Model-based Regularization
In the second part of the tutorial we investigate regularization approaches numerically. After introducing the classic Tikhonov approach, we focus on sparsity promoting regularization. Here, we consider Wavelet denoising and methods based on the so-called Total Variation, which is a common choice of regularizer for natural images. All approaches will be illustrated with hands-on coding examples, where the governing test problem is the CT reconstruction task.
Tutorial part 3 (2h): Data Driven Approaches
In the third part of the tutorial, we introduce data-driven and deep-learning based reconstruction approaches. We first learn about so-called post-processing strategies where we employ a typical U-Net architecture. Using a synthetic dataset, made up of simple shapes, we train a U-Net to solve a limited angle CT problem. Here, we identify both the great potential but also the pitfalls of learning based approaches. Finally, we consider plug-and-play methods, which combine model- and learning-based approaches.
Tutorial part 4 (2h): Uncertainty Quantification
In the fourth part of the tutorial, we consider the Bayesian viewpoint of inverse problems. We start by illustrating the fact that with changing noise vectors, also the reconstructed images vary. This introduces the concepts of a noise, prior and solution distribution. We explore sampling techniques and how they can help quantifying uncertainties in reconstructions.
Prerequisites
To participate in this course, you need to know
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basic knowledge in coding with Python and the Packages NumPy and PyTorch.
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how to run Python code in your own setup.
Target Group
This course is mainly for researchers and students interested in theory and application of mathematical image reconstruction.
Course Days & Times
Oct 6, 2025, 9 am - 5 pm
NOTE: Registration will open September 8, 2025, 12 pm.
Attendance & Certificates
The course content is coordinated, so we strongly recommend that you do not miss any part of the course. To receive a certificate we expect at least 80% attendance and active participation.
Registration & Cancellation
This course is open to individuals affiliated with Helmholtz or a HIDA Partner only.
Your registration for this course is binding. If you need to leave/miss the course for a period of time, please let us know in advance via hida-courses@helmholtz.de.
If you have to cancel the course for any reason, please do so as soon as possible to allow time for others to take your seat. To cancel, please withdraw your registration on the course site or write an email to hida-courses@helmholtz.de.
Additional Information
There is no waiting list for this course! If someone withdraws from a course, their place is automatically reopened. We therefore advise you to keep an eye on the registration in case the course is fully booked and you would like to attend. Also, this course will be offered again in the future - you can check our HIDA course catalog for updates.
This course is free of charge.
