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Researcher profile

Alexander Denker

Alexander Denker contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine Learningeess.IVGenomicsmath.NAmath.OCNumerical Analysis

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Published work

5 published item(s)

preprint2026arXiv

A Stability Benchmark of Generative Regularizers for Inverse Problems

Generative (diffusion) priors demonstrate remarkable performance in addressing inverse problems in imaging. Yet, for scientific and medical imaging, it is crucial that reconstruction techniques remain stable and reliable under imperfect settings. Typical definitions of stability encompass the notion of ''convergent regularization'', robustness to out-of-distribution data, and to inaccuracies in the forward operator or noise model. We evaluate these properties numerically. Furthermore, we benchmark generative approaches against modern optimization-based methods inspired by the widely used variational techniques. Our results give insights for which settings and applications generative priors can deliver state-of-the-art reconstructions, and on those in which they fall short or may even be problematic.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domains

Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such as resolution invariance and the ability to handle irregular discretisations. However, practical implementations have struggled to fully realise these benefits. Existing backbones like Fourier neural operators are often biased towards regular grids and fail to generalise to complex domain topologies. We propose a novel architecture for function-space diffusion models that represents generalised graph convolutional kernels as finite element functions, enabling the model to naturally handle unstructured meshes and complex geometries. We demonstrate the efficacy of our network architecture through a series of unconditional and conditional sampling experiments across diverse geometries, including non-convex and multiply-connected domains. Our results show that the proposed method maintains resolution invariance and achieves high fidelity in capturing functional distributions on non-trivial geometries.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Learning Regularization Functionals for Inverse Problems: A Comparative Study

In recent years, a variety of learned regularization frameworks for solving inverse problems in imaging have emerged. These offer flexible modeling together with mathematical insights. The proposed methods differ in their architectural design and training strategies, making direct comparison challenging due to non-modular implementations. We address this gap by collecting and unifying the available code into a common framework. This unified view allows us to systematically compare the approaches and highlight their strengths and limitations, providing valuable insights into their future potential. We also provide concise descriptions of each method, complemented by practical guidelines.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Feature reduction for machine learning on molecular features: The GeneScore

We present the GeneScore, a concept of feature reduction for Machine Learning analysis of biomedical data. Using expert knowledge, the GeneScore integrates different molecular data types into a single score. We show that the GeneScore is superior to a binary matrix in the classification of cancer entities from SNV, Indel, CNV, gene fusion and gene expression data. The GeneScore is a straightforward way to facilitate state-of-the-art analysis, while making use of the available scientific knowledge on the nature of molecular data features used.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Conditional Normalizing Flows for Low-Dose Computed Tomography Image Reconstruction

Image reconstruction from computed tomography (CT) measurement is a challenging statistical inverse problem since a high-dimensional conditional distribution needs to be estimated. Based on training data obtained from high-quality reconstructions, we aim to learn a conditional density of images from noisy low-dose CT measurements. To tackle this problem, we propose a hybrid conditional normalizing flow, which integrates the physical model by using the filtered back-projection as conditioner. We evaluate our approach on a low-dose CT benchmark and demonstrate superior performance in terms of structural similarity of our flow-based method compared to other deep learning based approaches.

0 citations0 reviewsNo code linkedOpen access