English Intern
  • Innenaufnahme der Teilbibliothek Mathematik
Inverse Probleme


  • (with R. Kretschmann): Maximum a posteriori testing in statistical inverse problems: arXiv: 2402.00686
  • (with C. König, A. Munk): Multiscale scanning with nuisance parameters: arXiv: 2307.13301
  • (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 H. Li): Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning: accepted for Inverse Problems, arXiv: 2304.10356
  • (with R. Kretschmann, D. Wachsmuth): Optimal regularized hypothesis testing in statistical inverse problems: Inverse Problems, Volume 40, Number 1, Dez. 2023, DOI 10.1088/1361-6420/ad1132
  • (with K. Proksch, J. Keller-Findeisen, H. Ta, A. Munk): Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees: Microscopy. dfad053, DOI: 10.1093/jmicro/dfad053
    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:  SIAM Journal on Scientific Computing Vol. 45, Issue 6, 2023
    DOI: 2207.13499
  • (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.

Nach oben

  • Inverse problems with Poisson data: Tikhonov-type regularization and iteratively regularized Newton methods, 2012 (Dissertation)

  • Ein neuer numerischer Ansatz zur L^p-Regularisierung, 2008 (Diplomarbeit)

(link zu meinen Zeitschriftenartikeln auf arXiv)
(link zu meiner MathSciNet Autorenseite)