Deutsch Intern
  • Group photo of the Team Inverse Problems
Inverse Problems

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
Portrait Frank Werner


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 H. Li, Frank Werner: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
  • (R. Kretschmann, D. Wachsmuth): Optimal regularized hypothesis testing in statistical inverse problems: arXiv: 2212.12897
  • (with N. K. Chada, M. A. Iglesias, S. Lu): On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data: arXiv: 2207.13499
  • (with K. Proksch, J. Keller-Findeisen, H. Ta, A. Munk): Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees: arXiv: 2207.13426
  • (with M. Pohlmann, A. Munk): Minimax detection of localized signals in statistical inverse problems: arXiv: 2112.05648

  • (with B. Hofmann, Y. Deng: On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case: Inverse Problems, Volume 39, Number 6, 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 Imaging125-143, 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 Imaging283-312 , 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.

To top

  • 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)

(link to my articles on arXiv)
(link to my MathSciNet author page)


Further Information


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

Academic Travels and Talks


  • Erskine-Fellowship at the University of Canterburry, Feb 17 - March 26, 2023, Christchurch, New Zealand




  • Chemnitz Symposium on Inverse Problems, integrated into the DMV-Jahrestagung, September 14-17, Chemnitz.









  • 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)


To top