Oleh Melnyk

Oleh Melnyk

Postdoctoral researcher

TU Berlin

Biography

After studying mathematics for financial and actuarial science for my bachelor’s, I realized that a change of direction is needed. So, I ended up in the math in data science master’s program at TU Munich. In those two years, I enjoyed the course on compressed sensing and, thus, wrote my master thesis with Felix Krahmer and Christian Kümmerle about the robustness of low-rank matrix recovery via basis pursuit. At that time, it was clear that this is the way, and I continued with doctoral studies on the topic of phase retrieval and ptychography under the joint supervision of Frank Filbir at Helmholtz Munich and Felix Krahmer at TU Munich. Four years later, I successfully defended my doctoral thesis and joined the group of Gabriele Steidl at TU Berlin.

Interests
  • Phase Retrieval
  • Compressed Sensing
  • Mathematical Imaging
  • Numerical Analysis
  • Optimization
Education
  • Doctoral Studies in Mathematics (Dr. rer. nat.), 2023

    Technical University of Munich/Helmholtz Center Munich

  • MSc in Mathematics in Data Science, 2018

    Technical University of Munich

  • BSc of Statistics, 2016

    Taras Shevchenko National University of Kyiv

Recent Publications

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(2024). Time-Harmonic Optical Flow with Applications in Elastography.

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(2024). Sparse additive function decompositions facing basis transforms. Foundations of Data Science.

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(2023). Image Recovery for Blind Polychromatic Ptychography. SIAM Journal on Imaging Sciences, Volume 16, Number 3, 1308-1337, 2023.

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(2022). Inverse Multislice Ptychography by Layer-wise Optimisation and Sparse Matrix Decomposition. IEEE Transactions on Computational Imaging, vol. 8, pp. 996-1011, 2022.

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(2022). On convergence of Ptychographic Iterative Engine for STFT phase retrieval. The 8th International Conference on Computational Harmonic Analysis 2022 (ICCHA2022).

(2022). On connections between Amplitude Flow and Error Reduction for phase retrieval and ptychography. Sampling Theory, Signal Processing, and Data Analysis, Volume 20, Article number: 16.

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(2022). On the robustness of noise-blind low-rank recovery from rank-one measurements. Linear Algebra and its Applications, Volume 652, Pages 37-81.

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(2022). On gradient-based methods for ptychography. Curves and Surfaces 2022.

(2021). On connections between Amplitude Flow and Error Reduction for phase retrieval. Online International Conference on Computational Harmonic Analysis (Online-ICCHA2021).

(2021). On Recovery Guarantees for Angular Synchronization. Journal of Fourier Analysis and Applications, Volume 27, Article number: 31.

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(2021). Stable ptychographic phase retrieval via lost subspace completion. 28th European Signal Processing Conference, p. 975, ISBN: 978-9-0827-9705-3.

(2020). Well-conditioned ptychographic imaging via lost subspace completion. Inverse Problems, Volume 36, Number 10.

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(2019). Phase retrieval from local correlation measurements with fixed shift length. 2019 13th International conference on Sampling Theory and Applications (SampTA).

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(2019). Phase retrieval from local correlation measurements with fixed shift length (OSA2019). OSA Technical Digest (Optica Publishing Group, 2019), paper MTu4D.3.

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