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Claudio Verdun

Claudio logotum.gif logoMath.gif
Position Doctoral Student
E-mail verdunematma.tum.de
Telephone +49 (0) 89 289 17989
Room 02.10.040
Address Faculty of Mathematics
Boltzmannstraße 3
85748 Garching (Munich)
Germany

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Conference Papers

C. Kümmerle and C. Mayrink Verdun. Denoising and Completion of Structured Low-Rank Matrices via Iteratively Reweighted Least Squares Pfeil, In International Traveling Workshop on Interactions between Low-Complexity Data Models and Sensing Techniques (iTWIST), Marseille, France, 2018.
Abstract
We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm optimizes an objective based on a non-convex surrogate of the rank by solving a sequence of quadratic problems. Our strategy combines computational efficiency, as it operates on a lower dimensional generator space of the structured matrices, with high statistical accuracy which can be observed in experiments on hard estimation and completion tasks. Our experiments show that the proposed algorithm StrucHMIRLS exhibits an empirical recovery probability close to 1 from fewer samples than the state-of-the-art in a Hankel matrix completion task arising from the problem of spectral super-resolution of badly separated frequencies. Furthermore, we explain how the proposed algorithm for structured low-rank recovery can be used as preprocessing step for improved robustness in frequency or line spectrum estimation problems.
BibTeX:
@inproceedings{KV18_iTwist18,
  author = {C. Kümmerle and C. Mayrink Verdun},
  title = {Denoising and Completion of Structured Low-Rank Matrices via Iteratively Reweighted Least Squares},
  booktitle = {International Traveling Workshop on Interactions between Low-Complexity Data Models and Sensing Techniques (iTWIST), Marseille, France},
  year = {2018}
}

News

2019
July 08–12 Talk at the Linear Algebra Without Borders (ILAS 2019) Pfeil in Rio de Janeiro, Brazil
2018
December 17–19 Vienna Workshop of Computational Optimization 2018 (VWCO18) Pfeil in Vienna, Austria
November 21–23 iTWIST: international Traveling Workshop on Interactions between low-complexity data models and Sensing Techniques Pfeil in Marseille, France
August 29–31 EURASIP Summer School Tensor-Based Signal Processing Pfeil in Leuven, Belgium
August 1–9 International Congress of Mathematicians 2018 (ICM 2018) Pfeil in Rio de Janeiro, Brasil
July 26–31 Asymptotic and Affine Geometric Analysis Pfeil in Rio de Janeiro, Brasil
June 18–22 Talk at the group of Prof. Amir Beck Pfeil at Tel-Aviv University in Tel-Aviv, Israel
June 12–13 Talk at the group of Prof. Daniel Potts Pfeil at TU Chemnitz in Chemnitz, Germany
February 26 – March 2 Winter School Modern Methods in Nonsmooth Optimization Pfeil in Würzburg, Germany
2017
November 29 - December 1 CoSIP Intense Course on Deep Learning Pfeil in Berlin, Germany
December 4–8 3. International Matheon Conference on Compressed Sensing and its Applications Pfeil in Berlin, Germany
July 13–19 Foundations of Computational Mathematics 2017 Pfeil in Barcelona, Spain
July 3–7 12th International Conference on Sampling Theory and Applications (SampTA 2017) Pfeil in Tallinn, Estonia
April 1 started his work as a doctoral student at the chair for Applied Numerical Analysis