Holder of the Professorship
Prof. Dr. Frank Werner
Holder of the Professorship
Professorship for Mathematics at the Chair of Mathematics IX
Emil-Fischer-Straße 30
97074
Würzburg
Building:
30 (Mathematik West)
Room:
00.008
Phone:
+49 931 31-87118
Fax:
+49 931 31-838430
Memberships
- EMS-TAG Inverse Problems (https://sites.google.com/view/ems-tag-ip)
- Gesellschaft für Inverse Probleme e.V. [ Society of Inverse Problems in German Speaking Countries] (http://inverseprobleme.de/)
Download Poster GIP - DMV-Fachgruppe Stochastik e.V. (http://www.fg-stochastik.de/home.html)
- IFIP Working group 7.4 - Inverse Problems and Imaging (http://www.ifip.org/bulletin/bulltcs/memtc07.htm#wg74)
- IPIA e.V. (https://www.ipia.site/)
Research Interests
My research is located at the interface between statistics and inverse problems, and I am particularly interested in the following topics:
- (Nonlinear) statistical inverse problems and regularization theory,
- uncertainty quantification by simultaneous (minimax) tests for inverse problems and
- applications in biophysics (e.g. fluorescence microscopy), especially with non-Gaussian noise.
- (with K. Bätz ): L^1 data fitting for Inverse Problems yields optimal rates of convergence in case of discretized white Gaussian noise: arXiv: 2511.11321
- (with E. Pfarr, R. Timofte ): Analyzing the Error of Generative Diffusion Models: From Euler-Maruyama to Higher-Order Schemes: arXiv: 2601.18425
- (with J. Dornbusch, E. Pfarr, F. Vasluianu, R. Timofte ): A Simple Combination of Diffusion Models for Better Quality Trade-Offs in Image Denoising, Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2025, pp. 895-904. CVPR 2025 open access repository:
Older version: available on arXiv: 2503.14654 - (with M. Warmuth, N. Lämmermann, C. Uhl): A Continuous and Robust Version of Dynamcial Component Analysis, Eur. Phys. J. Spec. Top. (2025). DOI: 10.1140/epjs/s11734-025-01911-6
- (with R. Kretschmann): Maximum a posteriori testing in statistical inverse problems: Inverse Problems and Imaging, Volume 19, Issue 6, 2025. DOI: 10.3934/ipi.2025015
Older version: available on arXiv: 2402.00686 - (with B. Hofmann):A Unified Concept of the Degree of Ill-posedness for Compact and Non-Compact Linear Operator Equations in Hilbert Spaces Under the Auspices of the Spectral Theorem: Numerical Functional Analysis and Optimization, Volume 46, Issue 4-5, pp. 322-347, 2025. DOI: 10.1080/01630563.2025.2451922
Older version: available on arXiv: 2408.01148 - (with C. Kanzow, F. Krämer, P. Mehlitz, G. Wachsmuth): Variational Poisson denoising via augmented Lagrangian methods: ETNA Electronic Transactions on Numerical Analysis, Volume 63, pp. 33–62, 2025. DOI: 10.1553/etna_vol63s33
Older version: available on arXiv: 2304.06434 - (with C. König, A. Munk): Multiscale scanning with nuisance parameters: Journal of the Royal Statistical Society: Series B, qkae100, 2024. DOI: 10.1093/jrsssb/qkae100
Older version: available on arXiv. - (with H. Li): Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning: Inverse Problems, , 025005, 2024. DOI 10.1088/1361-6420/ad12e0
Older version: available on arXiv: 2304.10356 - (with R. Kretschmann, D. Wachsmuth): Optimal regularized hypothesis testing in statistical inverse problems: , ,
Older version: available on arXiv. - (with K. Proksch, J. Keller-Findeisen, H. Ta, A. Munk): Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees. Editor's choice: Microscopy. dfad053, DOI: 10.1093/jmicro/dfad053
Older version: available on arXiv, DOI: 10.1093 - (with M. Pohlmann, A. Munk): Minimax detection of localized signals in statistical inverse problems: Information and Inference: A Journal of the IMA, Volume 12, Issue 3, September 2023, iaad026, DOI: 10.1093/imaiai/iaad026
- (with N. K. Chada, M. A. Iglesias, S. Lu): On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data: SIAM Journal on Scientific Computing Vol. 45, Issue 6, 2023. DOI: 2207.13499
Older version: available on arXiv - (with B. Hofmann, Y. Deng): On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case: , , DOI 10.1088/1361-6420/acd07b
Older version: available on arXiv - (with Y. Deng, B. Hofmann): Deautoconvolution in the two-dimensional case: ETNA. Volume 59, pp. 24-42, 2023, DOI: 10.1553/etna_vol59s24
Older version: available on arXiv - (with T. Hohage): Error estimates for variational regularization of Inverse Problems with general noise models for data and operator: ETNA. Volume 57, pp. 127-152, 2022, DOI: 10.1553/etna_vol57s127
- (with R. Siegmund, S. Jakobs, C. Geisler, A. Egner: isoSTED microscopy with water-immersion lenses and background reduction: Biophysical Journal. vol 120, Issue 14, 2021, DOI: 10.1016/j.bpj.2021.05.031
- (with M. Alamo, H. Li und Axel Munk): Variational multiscale nonparametric regression: Algorithms 2020, 13(11), 296. DOI: 10.3390/a13110296
Older version: available on arXiv - (with G. Kulaitis, A. Munk ): What is resolution? A statistical minimax testing perspective on super-resolution microscopy.
Annals of Statistics. 49(4): 2292-2312 (August 2021). DOI: 10.1214/20-AOS2037
Older version: available on arXiv: 2005.07450 - (mit S. Lu and P. Niu ): On the asymptotical regularization for linear inverse problems in presence of white noise.
In: SIAM/ASA Journal on Uncertainty Quantification. 1-28, vol 9, Issue 1, 2020. DOI: 10.1137/20M1330841 - (with F. Enikeeva, A. Munk and M. Pohlmann): Bump detection in the presence of dependency: Does it ease or does it load?. Bernoulli, 26 (2020), no. 4, 3280--3310. DOI: 10.3150/20-BEJ1226
Older version: available on arXiv. - (with A. Munk and T. Staudt): Statistical Foundations of Nanoscale Photonic Imaging. In: Nanoscale Photonic Imaging. 125-143, vol 134, Springer, 2020. DOI: 10.1007/978-3-030-34413-9_4
- (with A. Munk, H. Li and K. Proksch): Photonic imaging with statistical guarantees. From Multiscale Testing to Multiscale Estimation. In: Nanoscale Photonic Imaging. 283-312 , vol 134, Springer, 2020. DOI: 10.1007/978-3-030-34413-9_11
- (with H. Li): Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods. Annales de l’Institut Henri Poincaré, 56 (2020), no. 1, 405-427, 2020. DOI: 10.1214/19-AIHP966
Older version: available on arXiv. - (with C. König and A. Munk): Multidimensional multiscale scanning in Exponential Families: Limit theory and statistical consequences. The Annals of Statistics, 2020, Vol. 48, No. 2, 655-678. DOI: 10.1214/18-AOS1806
Older version: available on arXiv. - (with B. Hofmann): Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates. Inverse Problems 36 015004, 2020. DOI: 10.1088/1361-6420/ab4cd7
Older version: available on arXiv. - (with K. Proksch and A. Munk): Multiscale Scanning in Inverse Problems. The Annals of Statistics, 46(6B), 3569-3602, 2018. DOI: 10.1214/17-AOS1669
Older version: available on arXiv. - Adaptivity and Oracle Inequalities in Linear Statistical Inverse Problems: a (numerical) survey. In: New Trends in Parameter Identification for Mathematical Models, 291-316, Birkhäuser, 2018. DOI: 10.1007/978-3-319-70824-9_15
- (with F. Enikeeva and A. Munk): Bump detection in heterogeneous Gaussian regression. Bernoulli 24(2): 1266-1306, 2018. DOI: 10.3150/16-BEJ899
Older version: available on arXiv. - (with T. Hohage): Inverse Problems with Poisson Data: statistical regularization theory, applications and algorithms. Topical Review for Inverse Problems 32 093001, 2016. DOI: 10.1088/0266-5611/32/9/093001
- (with C. König and T. Hohage): Convergence Rates for Exponentially Ill-Posed Inverse Problems with Impulsive Noise. SIAM Journal on Numerical Analysis 54(1), 341-360, 2016. DOI: 10.1137/15M1022252
Older version: available on arXiv. - (with A. Munk): Discussion of "Hypothesis testing by convex optimization" by A. Goldenshluger, A. Juditsky and A. Nemirovski. Electronic Journal of Statistics 9(2): 1720-1722, 2015. DOI: 10.1214/14-EJS980
- On convergence rates for iteratively regularized Newton-type methods under a Lipschitz-type nonlinearity condition. Journal of Inverse and Ill-posed problems 23(1): 75-84, 2015. DOI: 10.1515/jiip-2013-0074
- (with T. Hohage): Convergence rates for Inverse Problems with Impulsive Noise. SIAM Journal on Numerical Analysis 52(3), 1203-1221, 2014. DOI: 10.1137/130932661
Older Version: available on arXiv. - (with T. Hohage): Iteratively regularized Newton-type methods with general data misfit functionals and applications to Poisson data. Numerische Mathematik 123(4), 745-779, 2013. DOI: 10.1007/s00211-012-0499-z
Older Version: available on arXiv. - (with T. Hohage): Convergence rates in expectation for Tikhonov-type regularization of Inverse Problems with Poisson data. Inverse Problems 28 104004, 2012. DOI: 10.1088/0266-5611/28/10/104004
Older Version: (Preprint), also available on arXiv.
- (with G. Kulaitis, A. Munk, F. Werner): A minimax testing perspective on spatial statistical resolution in microscopy. In Foundations of Modern Statistics, , Festschrift in Honor of Vladimir Spokoiny, Berlin, Germany, November 6–8, 2019)
- (with T. Hohage): Convergence in expectation results for phase retrieval problems in x-ray imaging. In Proceedings of the 11th International Conference on Mathematical and Numerical Aspects of Waves 139-140, 2013. (online version)
- Inverse Problems with Poisson data. In: Computational Inverse Problems, Oberwolfach Reports 9(4), 3115-3116, 2012. DOI: 10.4171/OWR/2012/51 (online version)
- Inverse problems with Poisson data: Tikhonov-type regularization and iteratively regularized Newton methods, 2012 (PhD thesis)
- Ein neuer numerischer Ansatz zur L^p-Regularisierung, 2008 (Diploma thesis - in German)
Education
| 2004 - 2009 | Studies of mathematics at the Georg-August-Universität Göttingen |
| 23.01.2009: | Examination (Diplom) in mathematics (passed with distinction) Thesis: "Ein neuer numerischer Ansatz zur Lp-Regularisierung" (in German) |
| 2009 - 2012 | PhD studies in mathematics at the Georg-August-Universität Göttingen Thesis: "Inverse Problems with Poisson data: Tikhonov-type regularization and iteratively regularized Newton methods" |
| 2012 - 2014 | Postdoctoral research fellow at the institute for numerical and applied mathematics |
| 2014 - 2020 | Group leader 'Statistical Inverse Problems in Biophysics' at the MPIBPC |
| 2020 - | Holder of the professorship "Inverse Problems" at the Chair of Scientific Computing in Würzburg |
I am married and father of two sons (*2012 and *2015)
Upcoming Events
- Organisation of "Sektion S28: Inverse Probleme" within the 96th Annual Meetings of the GAMM from March 16th to 20th, 2026 in Stuttgart
- Visiting Prof. Thorsten Hohage at Uni Göttingen, March 30-31, 2026
- Round Table Exchange on "Applied Mathematics" at KIT Karlsruhe, May 4-5, 2026
- Visiting Prof. Shuai Lu at the School of Mathematical Sciences, Fudan University, China, Oct 30 to Nov 7, 2026
Academic Travels and Talks
2026
- Vortrag am Gymnasium in Marktbreit am 13.02.2026 im Rahmen von "Mathematiker besuchen Ihre Schule" des Instituts für Mathematik
- Visiting Prof. Thorsten Hohage at Uni Göttingen, Jan. 4-6, 2026
2025
- Visiting Prof. Shuai Lu at the School of Mathematical Sciences, Fudan University, China, Oct 24 to Nov 1, 2025
- Visiting Prof. Roland Herzog und Vortrag im Optimization Seminar der Scientific Computing and Optimization (SCOOP) Group im "Interdisciplinary Center for Scientific Computing" (IWR) der Universität Heidelberg, Oct. 30 - Dec. 2, 2025
- 12th Applied Inverse Problems Conference (AIP2025) in Rio de Janeiro, July 28 to August 1, 2025 (Organisation Minisymposium und Vortrag)
- Workshop on Detecting Anomalous Structures in Stream Settings, DASS Workshop 2025, Lancaster University, 22 - 25 Sept 2025
- GIP Annual Meeting 2025, Universität des Saarlandes, 8 - 10 October 2025
- Visiting Prof. Angkana Rüland at University of Bonn, May 14.-16, 2025
- DFG Round Table “Applied Mathematics” at the University of Münster, May 12-13, 2025
- Vortrag am Johann-Schöner-Gymnasium in Karlstadt a. Main am 21.03.2025 im Rahmen von "Mathematiker besuchen Ihre Schule" des Instituts für Mathematik
- Visiting Prof. Thorsten Hohage at University of Göttingen, March 10.-12, 2025
- Talk "Statistical Inverse Problems - Regularization and Inference" at the Augsburger mathematisches Kolloquium, 05.02.2025
- 2025 Joint Mathematics Meetings (JMM 2025), Seattle, USA, January 8 to 11, 2025
2024
- Inverse Days 2024, Oulu, Finland, December 10–13, 2024
- GIP 2024 Annual Meeting, Siegen, September 25-27
- 11th International Conference "Inverse Problems: Modeling and Simulation(IPMS 2024), Malta, May 26 to June 01, 2024
- Research Visit TU Chemnitz, 29.-22.02.2024
2023
- Talk "Testing statistical hypothesis in Inverse Problems" in the Research Seminar at the Institute for Statistics and Operations Research, Dec 11, 2023 University of Vienna, Austria
- ICIAM 2023 Tokyo, Aug 20-25, 2023 Waseda University, Japan
- 11th Applied Inverse Problems Conference, 4.- 8. Sep. 2023 in Göttingen, Germany
- IWAP 2023, 10th International Workshop on Applied Probability, 7-10 June 2023, Thessaloniki, Greece
- Lecture in the Stochastical Colloquium, University Göttingen: "Testing statistical hypothesis in Inverse Problems", 31 May 2023
- Erskine-Fellowship at the University of Canterburry, Feb 17 - March 26, 2023, Christchurch, New Zealand
2022
- Lecture in the Mathematical Colloquium, University Bayreuth: "Inference in statistical Inverse Problems and applications to fluorescence microscopy", 3. Nov. 2022
- Symposium on Inverse Problems: From experimental data to models and back, Sep 19-21, Potsdam
- International Symposium on Nonparametric Statistics (ISNPS), June 20-24, Cyprus: "What is the resolution of a microscope?"
- International Conference Inverse Problems: Modeling and Simulation, May 22-28, Malta: "Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates"
- Visiting Bernd Hofmann at the TU Chemnitz, 29.03. - 01.04.
2021
- 2nd Alps-Adriatic Inverse Problems Workshop (AAIP 2021), September 22-24, Alpen-Adria-Universitaet Klagenfurt, Austria.
2020
- Chemnitz Symposium on Inverse Problems, integrated into the DMV-Jahrestagung, September 14-17, Chemnitz.
2019
- Talk in the Colloquium on Mathematics at the University of Mainz, December 05th: "Statistical Inverse Problems and applications to fluorescence microscopy"
- Chemnitz Symposium on Inverse Problems (on tour), September 30 - October 02, Frankfurt: "Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates" (slides)
- 2nd IMA Conference On Inverse Problems From Theory To Application, September 4-6, London, United Kingdom: "Convergence Analysis of (Statistical) Inverse Problems under Conditional Stability Estimates" (slides)
- European Meeting of Statisticians, July 22-26, Palermo, Italy: "Statistical Inference for Molecules: How many and Where?"
- Applied Inverse Problems Conference, July 08-12, Grenoble, France.
- Talk at the Berufenachmittag, January 15.
- Visiting Markus Reiß at the HU Berlin, January 7-9, talk in the research seminar on Mathematical Statistics: "Empirical Risk Minimization as Parameter Choice Rule for Filter-based Regularization Methods" (slides)
2018
- Visiting Bernd Hofmann at the TU Chemnitz, November 12-16: "Statistical Inference for Molecules: How many and Where?"
- Visiting Shuai Lu at the School of Mathematical Sciences of the Fudan University, September 03-16, Shanghai, China: "Statistical Inverse Problems and applications to fluorescence microscopy"
- Joint Statistical Meetings, July 28 - August 02, Vancouver, Canada: "Multiscale Scanning in Inverse Problems: Applications to super-resolution microscopy" (slides)
- Visiting Farida Enikeeva at the Probability and statistics lab of the Unversity of Poitiers, June 27-30.
- International Conference Inverse Problems: Modeling and Simulation, May 21-25, Malta: "Parameter identification problems with impulsive noise"
- Talk in the seminar Wirkung sucht Ursache at the University of Hamburg, May 08: "Was Fluoreszenz über den Ort und die Anzahl von Molekülen verrät"
- Lorentz Center workshop "Uncertainty Quantification in Complex, Nonparametric Statistical Models", April 16-20, Leiden, The Netherlands: "Statistical Inference for molecules: Where?" (slides)
- 13th German Probability and Statistics Days, February 27 - March 02, Freiburg, Germany: "Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods" (slides)
- Visiting Fabian Dunker at the School of Mathematics and Statistics of the University of Canterbury, February 12-16, Christchurch, New Zealand: "Statistical Inference for Molecules: How many, When and Where?"
2017
- Member of the organizing comittee of the Workshop "Statistics Meets Friends", November 29 - December 01, Göttingen (press release)
- New Trends In Parameter Identification for Mathematical Models (integrating the Chemnitz Symposium on Inverse Problems on tour), October 30 - November 03, IMPA, Rio de Janeiro, Brasil: "Unbiased Risk Estimation as a Parameter Choice Rule for Filter-based Regularization Methods" (slides) (video)
- Lorentz Center workshop "Bayesian and Nonlinear Inverse Problems", August 28 - September 01, Leiden, The Netherlands
- European Meeting of Statisticians, July 24-28, Helsinki, Finland: "Empirical Risk Minimization as Parameter Choice Rule for General Linear Regularization Methods" (slides)
- Applied Inverse Problems Conference, May 29 - June 2, Hangzhou, China: "Support inference in linear statistical Inverse Problems" (slides)
2016
- Chemnitz Symposium on Inverse Problems, September 22-23, Chemnitz: "Support inference in linear statistical Inverse Problems" (slides)
- International Conference Inverse Problems: Modeling and Simulation, May 23-28, Fethiye, Turkey
2015
- AMISTAT 2015 - Analytical Methods In Statistics, November 10-13, Prague: "Bump detection in heterogeneous Gaussian regression" (slides)
- European Meeting of Statisticians, July 6-10, Amsterdam: "Statistical Inference for Molecules: How many, when and where?"
- Applied Inverse Problems Conference, May 25-29, Helsinki: "Statistical methods in fluorescence microscopy"
- Visiting Farida Enikeeva at the Probability and statistics lab of the University of Poitiers, January 20-24, Poitiers: "Penalized likelihood estimators for Inverse Problems with Poisson data" (slides)
2014
- Chemnitz Symposium on Inverse Problems, Chemnitz, Germany: "Statistical Inverse Problems in fluorescence microscopy".
- International Conference Inverse Problems: Modeling and Simulation, Fethiye, Turkey: "Statistical regularization theory for Inverse Problems with Poisson data" (slides).
2013
- International Workshop on Inverse Problems and Regularization Theory, Shanghai, China: "Convergence rates for Inverse Problems with Impulsive Noise" (slides).
- Special Session New developments on inverse problems: Banach space setting and hybrid tomography imaging during the second week of the Colloquium of the Brazilian Mathematical Society at IMPA, Rio de Janeiro, Brazil: "Convergence rates for Inverse Problems with Impulsive Noise" (slides).
- Applied Inverse Problems Conference 2013, Daejeon, Korea: "Convergence Rates for Inverse Problems with Impulsive Noise" (slides).
2012
- November 16-25, 2012: Research stay at the Australian National University, Canberra, also joining the Canberra Symposium On Regularisation: "Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data" (slides).
- Oberwolfach workshop Computational Inverse Problems, Oberwolfach, Germany: "Inverse Problems with Poisson data"
- DMV Annual Meeting, Saarland University, Saarbrücken, Germany: "Convergence rates in expectation for Tikhonov-type regularization of inverse problems with Poisson data" (slides).
- PhD defense January 23rd: "Inverse Probleme mit Poisson Daten: Verallgemeinerte Tikhonov-Regularisierung und iterativ regularisierte Newton Methoden" (slides, german)
2011
- Chemnitz Symposium on Inverse Problems, Chemnitz, Germany: "Iteratively regularized Newton methods with general data misfit functionals and applications to Poisson data"
- Applied Inverse Problems Conference, College Station, Texas, USA: "Iteratively regularized Newton methods with general data misfit functionals and applications to Poisson data" (slides)
