Christian Kümmerle

In this context I have worked on lowrank matrix models, iteratively reweighted algorithms and highdimensional probability theory, and their applications to matrix completion, robust principal component analysis, compressed sensing and super resolution. You find some code about my research on GitHub ^{}.
Preprints
O. Guédon, F. Krahmer, C. Kümmerle, S. Mendelson and H. Rauhut. On the geometry of polytopes generated by heavytailed random vectors, arXiv:1907.07258, 2019.
[BibTeX] 
BibTeX:
@unpublished{GKKMR19, author = {Olivier Guédon, Felix Krahmer, Christian Kümmerle, Shahar Mendelson, Holger Rauhut}, title = {On the geometry of polytopes generated by heavytailed random vectors, year = {2019}, doi = {https://arxiv.org/abs/1907.07258} } 
F. Krahmer, C. Kümmerle and H. Rauhut. A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing, arXiv:1806.04261, 2018. 
Abstract At the same time, our results establish robustness of noiseblind l1decoders for recovering sparse vectors x from underdetermined, noisy linear measurements y=Ax+w under the weakest possible assumptions on the entrywise distributions that allow for recovery with optimal sample complexity even in the noiseless case. Our analysis predicts superior robustness behavior for measurement matrices with superGaussian entries, which we confirm by numerical experiments. 
BibTeX:
@unpublished{KrahmerKuemmerleRauhut18, author = {Felix Krahmer, Christian Kümmerle, Holger Rauhut}, title = {A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing}, year = {2018}, doi = {https://arxiv.org/abs/1806.04261} } 
Journal Articles
C. Kümmerle and J. Sigl. Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery, Journal of Machine Learning Research, 19(47):1−49, 2018. 
Abstract 
BibTeX:
@article{JMLR:v19:17244, author = {Christian K{\"u}mmerle and Juliane Sigl}, title = {Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery}, journal = {Journal of Machine Learning Research}, year = {2018}, volume = {19}, number = {47}, pages = {149}, url = {http://jmlr.org/papers/v19/17244.html} } 
Conference Papers
C. Kümmerle and C. Mayrink Verdun. Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares, In 13th International Conference on Sampling Theory and Applications (SampTA), 2019.
[BibTeX] 
BibTeX:
@inproceedings{KV19_SampTA19, author = {C. Kümmerle and J. Sigl}, title = {Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery}, booktitle = {13th International Conference on Sampling Theory and Applications (SampTA)}, year = {2019}, } 
C. Kümmerle and C. Mayrink Verdun. Denoising and Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares ^{}, In International Traveling Workshop on Interactions between LowComplexity Data Models and Sensing Techniques (iTWIST), Marseille, France, 2018. 
Abstract 
BibTeX:
@inproceedings{KV18_iTwist18, author = {C. Kümmerle and C. Mayrink Verdun}, title = {Denoising and Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares}, booktitle = {International Traveling Workshop on Interactions between LowComplexity Data Models and Sensing Techniques (iTWIST), Marseille, France}, year = {2018} } 
C. Kümmerle and J. Sigl. Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery, In 12th International Conference on Sampling Theory and Applications (SampTA), pp. 489493, 2017.
[BibTeX] 
BibTeX:
@inproceedings{HMIRLS_SampTA17, author = {C. Kümmerle and J. Sigl}, title = {Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery}, booktitle = {12th International Conference on Sampling Theory and Applications (SampTA)}, year = {2017}, pages = {489493} } 
News
2020  

From January  Postdoctoral Fellow at Johns Hopkins University, Department of Applied Mathematics & Statistics ^{} 
2019  
December 19  Doctoral Defense of my dissertation on Understanding and Enhancing Data Recovery Algorithms: From NoiseBlind Sparse Recovery to Reweighted Methods for LowRank Matrix Optimization 
OctoberDecember  Visiting Prof. Mauro Maggioni ^{} at Johns Hopkins University, Baltimore, USA 
September 1213  Workshop on LowRank Models and Applications (LRMA) ^{} in Mons, Belgium 
September 911  Visiting Prof. Ivan Markovsky ^{} at Vrije Universiteit Brussel, Belgium 
July 8–12  Invited Talk on Completion of Structured LowRank Matrices via Iteratively Reweighted Least Squares at the 13th International Conference on Sampling Theory and Applications (SampTA 2019) ^{} in Bordeaux, France 
2018  
December 17–19  Vienna Workshop of Computational Optimization 2018 (VWCO18) ^{} 
November 21–23  iTWIST: international Traveling Workshop on Interactions between lowcomplexity data models and Sensing Techniques ^{}, Marseille, France 
November 13  Oberseminar talk at the Applied Analysis Seminar ^{}, Universität Osnabrück 
October 14–19  Oberwolfach Seminar: Mathematics of Deep Learning ^{} 
September 12–13  Retreat of the groups of Prof. Holger Rauhut ^{} and Prof. Rudolf Mathar ^{} in Spa 
August 29–31  EURASIP Summer School TensorBased Signal Processing ^{} 
August 1–9  International Congress of Mathematicians 2018 (ICM 2018) ^{} 
July 26–31  Talk at the conference on Asymptotic and Affine Geometric Analysis ^{} in Rio de Janeiro, Brasil 
June 25–29  Visit at the group of Prof. Holger Rauhut ^{} at RWTH Aachen 
June 12–13  Visit at the group of Prof. Daniel Potts ^{} at TU Chemnitz 
June 11  New preprint about A Quotient Property for Matrices with HeavyTailed Entries and its Application to NoiseBlind Compressed Sensing ^{}, joint with Felix Krahmer and Holger Rauhut. 
March 25–31  Workshop on Applied Harmonic Analysis and Data Processing ^{} in Oberwolfach 
March 19–23  Talk at the 89th GAMM Annual Meeting ^{} about "SuperResolution meets Seismology: Seismic Data Interpolation via Structured LowRank Matrix Recovery" in Munich 
February 26 – March 2  Poster presentation at the Winter School Modern Methods in Nonsmooth Optimization ^{} about "Iteratively Reweighted Least Squares Algorithms for LowComplexity Matrix Recovery Problems" in Würzburg 
2017  
December 4–8  presenting a poster about The Quotient Property and the Robustness of \ell_1minimization under Weak Moment Assumptions at the 3. International Matheon Conference on Compressed Sensing and its Applications ^{} at TU Berlin, Berlin 
Sep. 4– Oct. 22 
visiting Prof. Jianwei Ma ^{} in Harbin, China 
July 13–19  presenting a poster at Foundations of Computational Mathematics 2017 ^{} in Barcelona, Spain 
July 3–7  giving a talk on Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery [slides] at the 12th International Conference on Sampling Theory and Applications (SampTA 2017) ^{} in Tallinn, Estonia 
June 5–8  presenting a poster at SPARS 2017 ^{} in Lisbon, Portugal 
March 16  submitted the paper ''Harmonic Mean Iteratively Reweighted Least Squares for LowRank Matrix Recovery'' [.pdf] together with my colleague Juliane Sigl. Supplementary code can be found here. 
2016  
July 18–22  participating in the Summer School on Mathematical Methods for HighDimensional Data Analysis at TU München 
June 27–July 1  participating in the Summer School on Regularization Methods for Machine Learning 2016 ^{} at University of Genoa, Italy 
April 18–22  participating in the Hausdorff School on Lowrank Tensor Techniques in Numerical Analysis and Optimization ^{} at Universität Bonn 
March 14–18  participating in the Workshop on Harmonic Analysis, Graphs and Learning ^{}, Hausdorff Research Institute for Mathematics, Bonn 
February 15–19  participating in the Workshop on Low Complexity Models in Signal Processing ^{}, Hausdorff Research Institute for Mathematics, Bonn 
February 12  coorganizing the Second Workshop DonauIsarInn: WDI²  Approximation Theory and Applications at TU München 
January 11–15  participating and presenting a poster at the Winter School on Advances in Mathematics of Signal Processing ^{}, Hausdorff Research Institute for Mathematics, Bonn 
January 4 – April 22  Guest researcher in the Special Trimester Program ”Mathematics of Signal Processing” ^{}, Hausdorff Research Institute for Mathematics, Bonn 
2015  
December 7–11  participating in the 2. International Matheon Conference on Compressed Sensing and its Applications ^{} at TU Berlin, Berlin 
December 3–5  attending the Winter School on Compressed Sensing 2015 ^{} at TU Berlin, Berlin 
October 26–30  participating in the conference "Convexity, probability and discrete structures, a geometric view point" ^{} in MarnelaVallée, France 
October 1  started his work as a doctoral student at the chair for Applied Numerical Analysis 