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 31-81491
Memberships
- Gesellschaft für Inverse Probleme e.V. [ Society of Inverse Problems in German Speaking Countries] (http://inverseprobleme.de/)
- 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. (http://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 C. König, A. Munk): Multiscale scanning with nuisance parameters: arXiv: 2307.13301
- (with H. Li): Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning: arXiv: 2304.10356
- (with C. Kanzow, F. Krämer, P.atrick Mehlitz, G. Wachsmuth): A Nonsmooth Augmented Lagrangian Method and its Application to Poisson Denoising and Sparse Control: arXiv: 2304.06434
- (with R. Kretschmann, D. Wachsmuth): Optimal regularized hypothesis testing in statistical inverse problems: arXiv: 2212.12897
- (with K. Proksch, J. Keller-Findeisen, H. Ta, A. Munk): Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees: accepted for publication by Oxford University Press.
arXiv: 2207.13426, 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, https://doi.org/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: accepted for SIAM Journal on Scientific Computing
DOI: 2207.13499 - (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
- (with Y. Deng, B. Hofmann): Deautoconvolution in the two-dimensional case: ETNA. Volume 59, pp. 24-42, 2023, DOI: 10.1553/etna_vol59s24
- (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
- (with G. Kulaitis, A. Munk ): What is resolution? A statistical minimax testing perspective on super-resolution microscopy
arXiv: 2005.07450. Annals of Statistics. 49(4): 2292-2312 (August 2021). DOI: 10.1214/20-AOS2037 - (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
- (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
- 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
Academic Travels and Talks
2023
- 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)
