Jürgen Frikel

Martin Storath, Andreas Weinmann, Jürgen Frikel et al.

We propose a new algorithmic approach to the non-smooth and non-convex Potts problem (also called piecewise-constant Mumford-Shah problem) for inverse imaging problems. We derive a suitable splitting into specific subproblems that can all be solved efficiently. Our method does not require a priori knowledge on the gray levels nor on the number of segments of the reconstruction. Further, it avoids anisotropic artifacts such as geometric staircasing. We demonstrate the suitability of our method for joint image reconstruction and segmentation. We focus on Radon data, where we in particular consider limited data situations. For instance, our method is able to recover all segments of the Shepp-Logan phantom from $7$ angular views only. We illustrate the practical applicability on a real PET dataset. As further applications, we consider spherical Radon data as well as blurred data.

Catyana Heyne, Jürgen Frikel, Filippo Riccio

Document type classification in visually rich documents remains challenging, as relevant information is distributed across textual, visual, and layout modalities. To capture this complexity, current approaches rely on diverse multimodal modeling strategies, resulting in heterogeneous architectures that complicate systematic comparison. This variability is also reflected in existing comparative studies, which often rely on heterogeneous evaluation setups, further complicating systematic comparison and making it difficult to assess progress. To address these limitations, this work provides a structured analysis of multimodal design strategies across transformer- and LLM-based architectures, combined with a controlled empirical comparison within a unified experimental framework. Specifically, four representative models (LayoutLMv3, Donut, Qwen3-VL-32B-Instruct, and Qwen3-32B) are evaluated on the RVL-CDIP benchmark to systematically analyze the contributions of text, image, and layout information for document type classification, with a particular focus on contrasting OCR-dependent and OCR-free approaches. The results show that specialized multimodal Transformers outperform LLM-based approaches on visually rich and layout-intensive documents. Image information contributes most strongly to reliable classification, while OCR-derived text provides useful but secondary support. These findings highlight that multimodal processing remains essential for documents with pronounced layout structure. Overall, the study provides a systematic basis for comparing multimodal architectures and offers practical guidance for selecting effective feature combinations and model designs for document type classification.

Wolfgang Erb, Andreas Weinmann, Mandy Ahlborg et al.

Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

Jürgen Frikel

We investigate the reconstruction problem of limited angle tomography. Such problems arise naturally in applications like digital breast tomosynthesis, dental tomography, electron microscopy etc. Since the acquired tomographic data is highly incomplete, the reconstruction problem is severely ill-posed and the traditional reconstruction methods, such as filtered backprojection (FBP), do not perform well in such situations. To stabilize the reconstruction procedure additional prior knowledge about the unknown object has to be integrated into the reconstruction process. In this work, we propose the use of the sparse regularization technique in combination with curvelets. We argue that this technique gives rise to an edge-preserving reconstruction. Moreover, we show that the dimension of the problem can be significantly reduced in the curvelet domain. To this end, we give a characterization of the kernel of limited angle Radon transform in terms of curvelets and derive a characterization of solutions obtained through curvelet sparse regularization. In numerical experiments, we will present the practical relevance of these results.

Simon Göppel, Jürgen Frikel, Markus Haltmeier

In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a severely ill-posed problem, the reconstructed images may suffer from characteristic artefacts or missing features, and significantly complicate subsequent image processing tasks (e.g., edge detection or segmentation). In this paper, we introduce a novel framework for the robust reconstruction of convolutional image features directly from CT data, without the need of computing a reconstruction firs. Within our framework we use non-linear (variational) regularization methods that can be adapted to a variety of feature reconstruction tasks and to several limited data situations . In our numerical experiments, we consider several instances of edge reconstructions from angularly undersampled data and show that our approach is able to reliably reconstruct feature maps in this case.