Matthias Wellershoff

Publications in peer-reviewed scientific journals

Rima Alaifari, Francesca Bartolucci and Matthias Wellershoff. Unique wavelet sign retrieval from samples without bandlimiting. Proceedings of the American Mathematical Society Series B, 11, July 2024. https://doi.org/10.1090/bproc/201.
Matthias Wellershoff. Phase retrieval of entire functions and its implications for Gabor phase retrieval. Journal of Functional Analysis, 286(11), June 2024. https://doi.org/10.1016/j.jfa.2024.110403.
Matthias Wellershoff. Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions. Journal of Mathematical Analysis and Applications, 530(2), February 2024. https://doi.org/10.1016/j.jmaa.2023.127692.
Rima Alaifari, Francesca Bartolucci, Stefan Steinerberger and Matthias Wellershoff. On the connection between uniqueness from samples and stability in Gabor phase retrieval. Sampling Theory, Signal Processing, and Data Analysis, 22(6), January 2024. https://doi.org/10.1007/s43670-023-00079-1.
Rima Alaifari, Francesca Bartolucci and Matthias Wellershoff. Phase retrieval of bandlimited functions for the wavelet transform. Applied and Computational Harmonic Analysis, 64:102-117, May 2023. https://doi.org/10.1016/j.acha.2023.01.002.
Matthias Wellershoff. Sampling at twice the Nyquist rate in two frequency bins guarantees uniqueness in Gabor phase retrieval. Journal of Fourier Analysis and Applications, 29(7), 2023. https://doi.org/10.1007/s00041-022-09990-y.
Rima Alaifari and Matthias Wellershoff. Phase retrieval from sampled Gabor transform magnitudes: counterexamples. Journal of Fourier Analysis and Applications, 28(9), 2021. https://doi.org/10.1007/s00041-021-09901-7.
Rima Alaifari and Matthias Wellershoff. Stability estimates for phase retrieval from discrete Gabor measurements. Journal of Fourier Analysis and Applications, 27(6), 2021. https://doi.org/10.1007/s00041-020-09802-1.
Rima Alaifari and Matthias Wellershoff. Uniqueness of STFT phase retrieval for bandlimited functions. Applied and Computational Harmonic Analysis, 50:34-48, January 2021. https://doi.org/10.1016/j.acha.2020.08.003.

Peer reviewed conference proceedings

Wojciech Czaja, Canran Ji, Shashank Sule and Matthias Wellershoff. Neural network-based speech reconstruction from undersampled STFT magnitude data. In 2024 32nd European Signal Processing Conference (EUSIPCO), Lyon, France, August 2024. IEEE. https://doi.org/10.23919/EUSIPCO63174.2024.10715072.
Rima Alaifari, Francesca Bartolucci and Matthias Wellershoff. Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(R). In 2023 International Conference on Sampling Theory and Applications (SampTA), New Haven, CT, USA, July 2023. IEEE. https://doi.org/10.1109/SampTA59647.2023.10301382.
Rima Alaifari and Matthias Wellershoff. On the stability of Gabor phase retrieval. In Proceedings of the 23rd International Congress on Acoustics, pages 3369--3376, Aachen, Germany, September 2019. Deutsche Gesellschaft für Akustik. https://doi.org/10.18154/RWTH-CONV-238869.
Rima Alaifari and Matthias Wellershoff. Ill-conditionedness of discrete Gabor phase retrieval and a possible remedy. In 2019 13th International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, July 2019. IEEE. https://doi.org/10.1109/SampTA45681.2019.9030891.

Contributions to conferences and seminars

Matthias Wellershoff. Quantitative bounds for sorting based permutation invariant embeddings. Talk at the 15th International Conference on Sampling Theory and Applications (SampTA), Vienna, Austria, July 2025.
Matthias Wellershoff. Uniqueness of phase retrieval from sampled STFT measurements: a short overview. Talk at Phase retrieval & Banach lattices, Zürich, Switzerland, May 2025.
Matthias Wellershoff. Stability of sorting based embeddings. Talk at Frame Theory Days 2024, St. Louis, MI, USA, October 2024.
Wojciech Czaja, Canran Ji, Shashank Sule and Matthias Wellershoff. Neural network-based speech reconstruction from undersampled STFT magnitude data. Poster at the 32nd European Signal Processing Conference, Lyon, France, August 2024.
Matthias Wellershoff. Unique wavelet sign retrieval from samples without bandlimiting. Hybrid talk in the Faraway Fourier Talks Online Seminar, College Park, MD, USA and online, May 2024.
Matthias Wellershoff. Uncovering the limits of uniqueness in sampled Gabor phase retrieval: A dense set of counterexamples in L2(R). Virtual talk at the 14th International Conference on Sampling Theory and Applications (SampTA), New Haven, CT, USA, July 2023.
Matthias Wellershoff. What’s new in wavelet phase retrieval. Talk at the International Conference on Approximation Theory and Beyond, Nashville, TN, USA, May 2023.
Rima Alaifari and Matthias Wellershoff. (Non-)Uniqueness in sampled Gabor phase retrieval. Winner of the Poster Session Awards at the Fall Fourier Talks 2022, College Park, MD, USA, October 2022.
Matthias Wellershoff. Uniqueness of phase retrieval from sampled Gabor measurements: a short overview. Talk in the Codes and Expansions (CodEx) Seminar, online, August 2022.
Matthias Wellershoff. Phase retrieval of entire functions. Talk at the 10th International Conference on Curves & Surfaces, Arcachon, France, July 2022.
Matthias Wellershoff. On the stability of Gabor phase retrieval. Talk at the 23rd International Congress on Acoustics, Aachen, Germany, September 2019.
Matthias Wellershoff. Ill-conditionedness of discrete Gabor phase retrieval and a possible remedy. Talk at the 13th International Conference on Sampling Theory and Applications (SampTA), Bordeaux, France, July 2019.
Matthias Wellershoff. Ill-conditionedness of discrete Gabor phase retrieval and a possible remedy. Talk at Aspects of Time-Frequency Analysis, Torino, Italy, June 2019.

Outreach activities

Matthias Wellershoff. Presentations by young researchers. Short talk at the ETH Day 2021, Zürich, Switzerland, November 2021.

Preprints

Matthias Wellershoff. On a dense set of functions determined by sampled Gabor magnitude. Preprint, July 2025. https://doi.org/10.48550/arXiv.2507.14556.
Marc Allain et al. Phasebook: A survey of selected open problems in phase retrieval. Preprint, May 2025. https://doi.org/10.48550/arXiv.2505.15351.
Radu Balan, Efstratios Tsoukanis and Matthias Wellershoff. Stability of sorting based embeddings. Preprint, October 2024. https://doi.org/10.48550/arXiv.2410.05446.
Matthias Wellershoff. Unknown pleasures: phase retrieval for time-frequency and time-scale structured data. Doctoral thesis, May 2022.
Matthias Wellershoff. Phase retrieval for audio processing applications. Master's thesis, April 2017.
Matthias Wellershoff. On the convergence rate of gradient descent for the computation of Riemannian averages. Bachelor's thesis, June 2015.

List of co-authors

Rima Alaifari, Marc Allain, Selin Aslan, Radu Balan, Francesca Bartolucci, Wim Coene, Wojciech Czaja, Sjoerd Dirksen, Jonathan Dong, Julien Flamant, Mark Iwen, Canran Ji, Felix Krahmer, Tristan van Leeuwen, Oleh Melnyk, Andreas Menzel, Allard P. Mosk, Viktor Nikitin, Palina Salanevich, Gerlind Plonka, Stefan Steinerberger, Sashank Sule, Efstratios Tsoukanis

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