University of Göttingen - Institute for Numerical and Applied Mathematics
Gerlind Plonka-Hoch

Own homepage

Current projects
EXPOWER: EXPOnential analysis emPOWERing innovation (2021-2025)
EU project (H2020-MSCA-RISE)
Low-rank and sparsity-based models in Magnetic Resonance Imaging (2021-2024)
DFG project (subproject B03) within the CRC 1456 (Mathematics of Experiment, first funding period)
Discovering structure in complex data: Statistics meets Optimization and Inverse Problems (2015-2024)
DFG Research Training Group 2088 (RTG 2088)
OCT-let: Designing an Optimum Sparse Representation for Ophthalmic Optical Coherence Tomography Image Analysis (2020-2023)
Georg Forster Research Fellowship for Professor Hossein Rabbani (Isfahan University of Medical Sciences)
Teaching
Research seminar: Numerical Analysis (English) (WS 2021/2022)
Thursday 12.30 - 14.00, online (2 SWS)
Lecture: Image and Geometry Processing III (English) (WS 2021/2022)
Tuesday and Friday 10.15 - 11.55, online (Lecture: 4 SWS + Exercises: 2 SWS SWS / 9 ECTS)
Publications
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
Nadiia Derevianko, Gerlind Plonka, Markus Petz
University of Göttingen, Institute for Numerical and Applied Mathematics, 2021 (preprint available at arXiv)
Frame soft shrinkage operators are proximity operators
Jakob Geppert, Gerlind Plonka
University of Göttingen, Institute for Numerical and Applied Mathematics, 2019 (preprint available at arXiv)
Exact Reconstruction of Extended Exponential Sums Using Rational Approximation of their Fourier Coefficients
Nadiia Derevianko, Gerlind Plonka
Analysis and Applications, accepted, 2021 (preprint available at arXiv)
Statistical modeling of retinal optical coherence tomography using the Weibull mixture model
Sahar Jordani, Zahra Amini, Gerlind Plonka, Hossein Rabbani
Biomedical Optics Express 12(9), 5470-5488, 2021 (open access https://doi.org/10.1364/BOE.430800)
Optimal Rank-1 Hankel Approximation of Matrices: Frobenius Norm and Spectral Norm and Cadzow's Algorithm
Hanna Knirsch, Markus Petz, Gerlind Plonka
Linear Algebra Appl. 629, 1-39, 2021 (preprint available at arXiv)
Exact Reconstruction of Sparse Non-Harmonic Signals from their Fourier Coefficients
Markus Petz, Gerlind Plonka, Nadiia Derevianko
Sampling Theory, Signal Processing, and Data Analysis 19, 7 (open access), 2021 (preprint available at arXiv)
Deterministic Sparse Sublinear FFT with Improved Numerical Stability
Gerlind Plonka, Therese von Wulffen
Results Math. 76(2), 53, 2021 (open access https://doi.org/10.1007/s00025-020-01330-0)
Modifications of Prony's Method for the Recovery and Sparse Approximation of Generalized Exponential Sums
Ingeborg Keller, Gerlind Plonka
G.E. Fasshauer et al. (eds.), Approximation Theory XVI, Springer Proceedings in Mathematics & Statistics 336, 2021 (preprint as download)
The Difference between Optimal Rank-1 Hankel Approximations in the Frobenius Norm and the Spectral Norm
Hanna Knirsch, Markus Petz, Gerlind Plonka
Proc. Appl. Math. Mech. Volume 20, 85-86, 2020 (DOI 10.1002/pamm.202000085)
Iterative Sparse FFT for M-sparse Vectors: Deterministic versus Random Sampling
Gerlind Plonka, Therese von Wulffen
Proc. Appl. Math. Mech. Volume 20, 134-135, 2020 (DOI 10.1002/pamm.202000134)
Parseval proximal neural networks
Marzieh Hasannasab, Johannes Hertrich, Sebastian Neumayer, Gerlind Plonka, Simon Setzer, Gabriele Steidl
Fourier Anal Appl 26, 59, 2020 (preprint available at arXiv)
A tree-based dictionary learning framework
Renato Budinich, Gerlind Plonka
International Journal of Wavelets, Multiresolution and Information Processing 2050041, 2020 (preprint as download)
One-dimensional discrete-time phase retrieval
Robert Beinert, Gerlind Plonka
In: Salditt T., Egner A., Luke D. (eds) Nanoscale Photonic Imaging. Topics in Applied Physics, vol 134. Springer, Cham, pp. 603-627, 2020 (preprint as download)
The Generalized Operator-Based Prony Method
Kilian Stampfer, Gerlind Plonka
Constructive Approximation 52, 247-287, 2020 (preprint as download)
Frame soft shrinkage as proximity operator
Marzieh Hasannasab, Sebastian Neumayer, Gerlind Plonka, Simon Setzer, Gabriele Steidl, Jakob Geppert
University of Göttingen, Institute for Numerical and Applied Mathematics, 2019 (preprint available at arXiv)
Reconstruction of Non-Stationary Signals by the Generalized Prony Method
Ingeborg Keller, Gerlind Plonka, Kilian Stampfer
Proc. Appl. Math. Mech. Volume 19, 358--359, 2019 (DOI 10.1002/pamm.201900358)
Computation of adaptive Fourier series by sparse approximation of exponential sums
Gerlind Plonka, Vlada Pototskaia
Journal of Fourier Analysis and Applications 25(4), pp. 1580–1608, 2019 (preprint as download)
Real Sparse Fast DCT for Vectors with Short Support
Sina Bittens, Gerlind Plonka
Linear Algebra and its Applications 582, pp.359-390, 2019 (preprint as download (arXiv))
Optimal approximation with exponential sums by maximum likelihood modification of Prony's method
Ran Zhang, Gerlind Plonka
Advances in Computational Mathematics 45(3), 1657-1687, 2019 (revised preprint as download)
Reconstruction of stationary and non-stationary signals by the generalized Prony method
Gerlind Plonka, Kilian Stampfer, Ingeborg Keller
Analysis and Applications 17(2), 179-210, 2019 (revised preprint as download)
further publications...
Software
Easy Path Wavelet Transform (EPWT)
Wavelet shrinkage on paths for denoising of scattered data including an adaptive deterministic and an adaptive random path construction.
Dennis Heinen, Gerlind Plonka, Stefanie Tenorth
Sparse FFT (small support)
A new deterministic sparse FFT algorithm for vectors with small support.
Katrin Wannenwetsch, Gerlind Plonka
Sparse FFT (real non-negative)
A new deterministic sparse FFT algorithm for real non-negative vectors.
Katrin Wannenwetsch, Gerlind Plonka
Deterministic Sparse FFT
Deterministic sparse FFT for M-sparse vectors, implemented in MATLAB.
Gerlind Plonka, Katrin Wannenwetsch
Sparse Fast DCT for Vectors with One-block Support
Sparse fast DCT algorithm for vectors with one-block support, implemented in MATLAB and Python.
Sina Bittens, Gerlind Plonka
Sparse FFT for Vectors with Reflected Two-block Support
Sparse FFT algorithm for vectors with reflected two-block support, implemented in MATLAB and Python.
Sina Bittens, Gerlind Plonka
Real Sparse DCT for Vectors with Short Support
Real sparse DCT algorithm for vectors with short support, implemented in MATLAB and Python.
Sina Bittens, Gerlind Plonka
Deterministic Sparse Sublinear FFT with Improved Numerical Stability
Deterministic sparse sublinear FFT for M-sparse vectors with improved numerical stability, implemented in Python.
Gerlind Plonka, Therese von Wulffen
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients, implemented in MATLAB.
Markus Petz, Gerlind Plonka, Nadiia Derevianko
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients, implemented in MATLAB.
Nadiia Derevianko, Gerlind Plonka
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation, implemented in MATLAB.
Nadiia Derevianko, Gerlind Plonka, Markus Petz



Prof. Dr. Gerlind Plonka-Hoch

University of Göttingen
Institute for Numerical and Applied Mathematics
Lotzestr. 16-18
37083 Göttingen
Raum 117

Tel.: 0551-39-26777
plonka AT math.uni-goettingen.de