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Inverse Problems


  • Remo Kretschmann, Daniel Wachsmuth, Frank Werner: Optimal regularized hypothesis testing in statistical inverse problems: arXiv: 2212.12897
  • Bernd Hofmann, Frank Werner, Yu Deng: On uniqueness and ill-posedness for the deautoconvolution problem in the multi-dimensional case: arXiv: 2212.06534
  • Yu Deng, Bernd Hofmann, Frank Werner: Deautoconvolution in the two-dimensional case: arXiv: 2210.14093v1
  • Neil K. Chada, Marco A. Iglesias, Shuai Lu, Frank Werner: On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data: arXiv: 2207.13499
  • Katharina Proksch, Frank Werner, Jan Keller-Findeisen, Haisen Ta, Axel Munk: Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees: arXiv: 2207.13426
  • G. Kulaitis, A. Munk, F. Werner: A minimax testing perspective on spatial statistical resolution in microscopy
  • M. Pohlmann, F. Werner, A. Munk: Minimax detection of localized signals in statistical inverse problems: arXiv: 2112.05648

  • (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.

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  • (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)

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