Publications
- (with B. Hofmann): A unified concept of the degree of ill-posedness for compact and non-compact linear operators in Hilbert spaces under the auspices of the spectral theorem: arXiv: 2408.01148
- (with R. Kretschmann): Maximum a posteriori testing in statistical inverse problems: arXiv: 2402.00686
- (with C. Kanzow, F. Krämer, P. Mehlitz, G. Wachsmuth): A Nonsmooth Augmented Lagrangian Method and its Application to Poisson Denoising and Sparse Control: arXiv: 2304.06434
- (with C. König, A. Munk): Multiscale scanning with nuisance parameters: Journal of the Royal Statistical Society: Series B, qkae100, 2024. DOI: 10.1093/jrsssb/qkae100
Older version: available on arXiv. - (with H. Li): Adaptive minimax optimality in statistical inverse problems via SOLIT -- Sharp Optimal Lepskii-Inspired Tuning: Inverse Problems, , 025005, 2024. DOI 10.1088/1361-6420/ad12e0
Older version: available on arXiv: 2304.10356 - (with R. Kretschmann, D. Wachsmuth): Optimal regularized hypothesis testing in statistical inverse problems: , ,
Older version: available on arXiv. - (with K. Proksch, J. Keller-Findeisen, H. Ta, A. Munk): Towards quantitative super-resolution microscopy: Molecular maps with statistical guarantees. Editor's choice: Microscopy. dfad053, DOI: 10.1093/jmicro/dfad053
Older version: available on arXiv, 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, DOI: 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
Older version: available on arXiv - (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
Older version: available on arXiv - (with Y. Deng, B. Hofmann): Deautoconvolution in the two-dimensional case: ETNA. Volume 59, pp. 24-42, 2023, DOI: 10.1553/etna_vol59s24
Older version: available on arXiv - (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
Older version: available on arXiv - (with G. Kulaitis, A. Munk ): What is resolution? A statistical minimax testing perspective on super-resolution microscopy.
Annals of Statistics. 49(4): 2292-2312 (August 2021). DOI: 10.1214/20-AOS2037
Older version: available on arXiv: 2005.07450 - (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
Older Version: available on arXiv. - (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)
