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Publications

Publications

Papers in refereed journals

• D. Gerth Using Landweber method to quantify source conditions - a numerical study,Journal of Inverse and ill-posed Problems, published ahead of print, DOI:10.1515/jiip-2018-0071 2018
• J. Flemming and D. Gerth Injectivity and weakâˆ—-to-weak continuity suffice for convergence rates in l1-regularization, Journal of Inverse and ill-posed Problems 26 (1) p. 85-94, DOI:10.1515/jiip-2017-0008, 2018
• D. Gerth Convergence rates for l1-regularization without the help of a variational inequality, Electronic Transactions on Numerial Analysis 46 p. 233-244, Fulltext, 2017
• D. Gerth, A. Hofinger and R. Ramlau On the lifting of deterministic convergence rates for inverse problems with stochastic noise, Inverse Problems and Imaging 11 (4) p. 663-687, DOI:10.3934/ipi.2017031, 2017
• S. Birkholz, G. Steinmeyer, S. Koke, D. Gerth, S. Bürger and B. HofmannRegularization of an autoconvolution problem in ultrashort laser pulse characterization, Journal of the Optical Society of America B 32 (5) p. 983-992, DOI: 10.1364/JOSAB.32.000983, 2015
• D. Gerth, B. Hahn and R. Ramlau The method of the approximate inverse for atmospheric tomography, Inverse Problems 31 (6) 065002, DOI:10.1088/0266-5611/31/6/065002, 2015
• D. Gerth, E. Klann, L. Reichel and R. Ramlau On fractional Tikhonov regularization, Journal of Inverse and Ill-posed Problems 30, ahead of print, published online, DOI: 10.1515/jiip-2014-0050, 2015
• D. Gerth and R. Ramlau A stochastic convergence analysis for Tikhonov regularization with sparsity constraints, Inverse Problems 30 (5) 055009, DOI:10.1088/0266-5611/30/5/055009, 2014
• D. Gerth, B. Hofmann, S. Birkholz, S. Koke and G. Steinmeyer Regularization of an autoconvolution problem in ultrashort laser pulse characterization, Inverse Problems in Science and Engineering 22 (2) p. 245-266, DOI: 10.1080/17415977.2013.769535, 2014

Submitted articles

• D. Gerth and B. Hofmann Oversmoothing regularization with $\ell^1$-penalty term, submitted to AIMS Mathematics
• D. Gerth, E. Escoto, G. Steinmeyer and B. Hofmann Regularized Differential Evolution for a blind phase retrieval problem in ultrashort laser pulse characterization, submitted to Review of Scientific Instruments

Theses

• D. Gerth: Problem-adapted Regularization for Inverse problems in the Deterministic and Stochastic Setting, Dissertation, Johannes Kepler University Linz, Austria, September 2015, (PDF)
• D. Gerth: Regularization of an autoconvolution problem occurring in measurements of ultra-short laser pulses, Diploma thesis, Chemnitz University of Technology, September 2011 (PDF)