# 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:*, Volume 12, Issue 3, September 2023, iaad026, https://doi.org/10.1093/imaiai/iaad026*A Journal of the IMA* - (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:
- (with Y. Deng, B. Hofmann): Deautoconvolution in the two-dimensional case:
Volume 59, pp. 24-42, 2023, DOI: 10.1553/etna_vol59s24.*ETNA* - (with T. Hohage): Error estimates for variational regularization of Inverse Problems with general noise models for data and operator:
Volume 57, pp. 127-152, 2022, DOI: 10.1553/etna_vol57s127.*ETNA* - (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 L^{p}-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)