Topic Day „Mathematics in Imaging“

September 06, 2024
Location: Alte Mensa (Wilhelmsplatz 3, 37073 Göttingen)

Imaging techniques are used in many fields of science and technology such as microscopy, astronomy, MRI, remote sensing, or structure health monitoring to process and extract information from images and to reconstruct such images from indirect data. In many aspects of the field tremendous progress has been achieved in last years by the use of machine learning techniques. The aim of this Topic Day is to provide insight into mathematical problems and challenges as well as potentials and limitations of mathematical approaches in imaging by leading experts in the field.

Scientific Program:

13:30-13:40 opening

13:40-14:40 Gabriele Steidl (Technical University of Berlin)

Gradient flows, non-smooth kernels and generative models for posterior sampling in inverse problems

Abstract: This talk is concerned with inverse problems in imaging from a Bayesian point of view, i.e. we want to sample from the posterior given noisy measurement. We tackle the problem by studying gradient flows of particles in high dimensions. More precisely, we analyze Wasserstein gradient flows of maximum mean discrepancies defined with respect to different kernels, including non-smooth ones.In high dimensions, we propose the efficient flow computation via Radon transform (slicing) and subsequent sorting or Fourier transform at nonequispaced knots. Special attention is paid to non-smooth Riesz kernels.

We will see that Wasserstein gradient flows of corresponding maximum mean discrepancies have a rich structure. In particular, singular measures can become absolutely continuous ones and conversely. Finally, we approximate our particle flows by conditional generative neural networks and apply them for conditional image generation and in inverse image restoration problems like computerized tomography and superresolution.

14:40-15:00 coffee break

15:00-16:00 Otmar Scherzer (University of Vienna)

Data driven regularization by projection

Abstract: We study linear inverse problems under the premise that the forward operator is not at hand but given indirectly through some input-output training pairs. We demonstrate that regularization by projection can be formulated using the training data only, without making use of the forward operator.  We study convergence and stability of the regularized solutions.
We also provide some numerical results, which show the feasibility of this approach.
This is joint work with Andrea Aspri (Milan), Leon Frischauf (Vienna),  Yury Korolev (Bath)

16:00-16:15 coffee break

16:15-17:15 Gitta Kutyniok (Ludwig-Maximilian-University Munich)

Imaging and AI: From Reliability to Next Generation Computing

Abstract: The new wave of artificial intelligence is impacting all aspects of imaging science in an unprecedented manner. However, one current major drawback is the lack of reliability as well as the enormous energy problem.

In this lecture we will first provide an introduction into this vibrant research area. We will then present some recent advances, in particular, concerning optimal combinations of traditional model-based methods with AI-based approaches in the sense of true hybrid algorithms, with a particular focus on limited-angle computed tomography. Due to the necessity to consider energy-efficient next generation computing in imaging, we will also touch upon the topics of neuromorphic computing and spiking neural networks.

17:30-19:30 DMV Präsidiumssitzung

17:30-19:00 Guided walk through Göttingen and its mathematical history lead by Prof. Dr. Gert Lube

20:00 Dinner at Restaurant Bullerjahn (Markt 9, 37073 Göttingen)

Registration:

crc1456@uni-goettingen.de

• first name, last name, title
  
• Do you want to participate at the guided walk through Göttingen and its mathematical history?
  
• Do you want to participate at the dinner at Bullerjahn?