Prof. Dr. rer. nat. Jürgen Frikel

Current semester (Winter 2026/27)

• Mathematical Methods in Modern AI and Applications

Previous courses

• Inverse Problems and Imaging · Integral Transforms and Applications · Image Processing · Linear Methods in AI · Nonlinear Methods in AI · Analysis I and II · Mathematics I and II

All course materials are available on ELO.

Thesis TOPICS

I offer bachelor’s and master’s theses and research projects closely linked to my current research in the following areas:

• Mathematical imaging and inverse problems: reconstruction from incomplete data, learning-based reconstruction and regularization, frame-based methods
• Computer vision and modern AI: representation learning, self-supervised learning, domain adaptation for industrial imaging
• Document analysis and information extraction: multimodal foundation models, synthetic data generation, domain adaptation
• Mathematical foundations: Fourier and harmonic analysis, integral transforms, functional analysis, numerical analysis

Interested? Theses in cooperation with companies are explicitly welcome, as are your own topic proposals. Simply send me an email with your topic idea, your degree program, and a few suggested dates for a meeting. See also the IMDS Lab.

Research Interests

My research focuses on mathematical foundations, methodology, and algorithms in the following areas:

• Mathematical imaging and inverse problems: image reconstruction from incomplete data, learning-based reconstruction and regularization, frame-based methods, microlocal analysis
• Computer vision and modern AI: representation learning, self-supervised learning, domain adaptation, industrial imaging
• Document analysis and information extraction: multimodal foundation models, synthetic data generation, domain adaptation

Memberships

• Gesellschaft für Inverse Probleme e.V. (GIP) – Inverse Problems Society of the German-Speaking Countries
• Society for Industrial and Applied Mathematics (SIAM) and SIAM Activity Group on Imaging Science (SIAG/IS)

A complete list of my publications is available on my Google Scholar profile. See also my profiles on ORCID and ResearchGate.

Publications & Preprints 2026

• T. Selig, P. Bauer, T. März, M. Storath, J. Frikel, A. Weinmann: Filter-Free Two-Stage Reconstruction for Low-Dose CT Across Regular and Irregular Sparse-Angle Sampling. Sensing and Imaging 27, Article 152, 2026. DOI: 10.1007/s11220-026-00834-3
• J. Frikel, S. Göppel, M. Haltmeier: Data-Proximal Null-Space Networks for Inverse Problems. Submitted, 2026. arXiv:2309.06573
• N. Keltsch, J. Schwab, B. Walder, S. Göppel, J. Frikel, M. Haltmeier: Adversarial Stability of Null-Space and Residual Networks. Submitted, 2026.
• M. Schön, S. Hipp, J. Frikel: Curvelet-Domain Analysis of Antenna Array Responses. Submitted, 2026.
• F. Riccio, J. Frikel: Industrial Anomaly Detection: A Case Study on the Limits of Normal-Only Adaptation. Submitted, 2026.
• J. Frikel, F. Riccio: Category Structure in Self-Supervised Industrial Image Representations: A Preliminary Study. Submitted, 2026.
• C. Heyne, J. Frikel, F. Riccio: Multimodal Approaches for Visually-Rich Document Type Classification: A Comparative Analysis. Preprint, 2026. arXiv:2606.02162

Most cited publications

• J. Frikel, E. T. Quinto: Characterization and Reduction of Artifacts in Limited Angle Tomography. Inverse Problems 29(12), 125007, 2013. DOI: 10.1088/0266-5611/29/12/125007
• M. Storath, A. Weinmann, J. Frikel, M. Unser: Joint Image Reconstruction and Segmentation Using the Potts Model. Inverse Problems 31(2), 025003, 2015. DOI: 10.1088/0266-5611/31/2/025003
• J. Frikel: Sparse Regularization in Limited Angle Tomography. Applied and Computational Harmonic Analysis 34(1), 117–141, 2013. DOI: 10.1016/j.acha.2012.03.005
• L. Borg, J. Frikel, J. S. Jørgensen, E. T. Quinto: Analyzing Reconstruction Artifacts from Arbitrary Incomplete X-ray CT Data. SIAM Journal on Imaging Sciences 11(4), 2786–2814, 2018. DOI: 10.1137/18M1166833
• J. Frikel, M. Haltmeier: Efficient Regularization with Wavelet Sparsity Constraints in Photoacoustic Tomography. Inverse Problems 34(2), 024006, 2018. DOI: 10.1088/1361-6420/aaa0ac

Invided Talks 2026

• Data-Proximal Reconstructions in Tomography. AMS Special Session on Tomography Theory and Applications in Honor of Todd Quinto’s 75th Birthday, Joint Mathematics Meetings (JMM 2026), Washington, D.C., USA, January 2026.
• A Data-Proximal Learning Framework for Inverse Problems. Workshop “Applications of Tomographic Methods,” Erwin Schrödinger International Institute for Mathematics and Physics (ESI), University of Vienna, Austria, June 2026.
• Category Structure in Self-Supervised Industrial Image Representations: A Preliminary Study (joint work with F. Riccio). 4th Symposium on Recent Trends in Inverse Problems in Imaging and Computer Vision: From Modeling to Applications, ICNAAM 2026, Heraklion, Crete, Greece, September 2026.
• G-Frame-Based Inversion of the Radon Transform Minisymposium “Generalized Radon Transforms and Microlocal Analysis in Tomography,” SIAM Conference on Imaging Science (IS26), Salt Lake City, UT, USA, November 2026.

   

Academic positions

• since 2021 · Research Professorship, OTH Regensburg
• since 2016 · Professor of Applied Mathematics, OTH Regensburg
• 2015–2016 · H. C. Ørsted Postdoctoral Fellow, DTU Compute, Technical University of Denmark
• 2014 · Researcher and Lecturer, Tufts University, USA
• 2010–2015 · Researcher, Technical University of Munich and Helmholtz Zentrum München

Industry

• 2008–2010 · Software Engineer, GE Healthcare, Munich
• 2005–2007 · Software Engineer (working student), Siemens Corporate Technology, Munich

Education

• 2013 · Dr. rer. nat. in Mathematics, Technical University of Munich (summa cum laude)
• 2007 · Diplom in Mathematics, Technical University of Munich (with distinction)