7 papers
A neural operator view on U-Nets for inverse imaging problems
Alexander Auras, Martin Burger, Samira Kabri +2
Deep neural networks have shown great empirical success in the solution of a wide variety of ill-posed inverse problems in imaging. Yet, very few works have studied their behavior…
Allure of Craquelure: A Variational-Generative Approach to Crack Detection in Paintings
Laura Paul, Holger Rauhut, Martin Burger +2
Recent advances in imaging technologies, deep learning and numerical performance have enabled non-invasive detailed analysis of artworks, supporting their documentation and conserv…
Explainable Learning Based Regularization of Inverse Problems
Martin Burger, Samira Kabri, Gitta Kutyniok +2
Machine learning techniques for the solution of inverse problems have become an attractive approach in the last decade, while their theoretical foundations are still in their infan…
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
Martin Burger, Samira Kabri, Yury Korolev +2
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns…
Learned Regularization for Inverse Problems: Insights from a Spectral Model
Martin Burger, Samira Kabri
In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction oper…
Resolution-Invariant Image Classification based on Fourier Neural Operators
Samira Kabri, Tim Roith, Daniel Tenbrinck +1
In this paper we investigate the use of Fourier Neural Operators (FNOs) for image classification in comparison to standard Convolutional Neural Networks (CNNs). Neural operators ar…
Convergent Data-driven Regularizations for CT Reconstruction
Samira Kabri, Alexander Auras, Danilo Riccio +4
The reconstruction of images from their corresponding noisy Radon transform is a typical example of an ill-posed linear inverse problem as arising in the application of computerize…