Current and recent projects
- FELFocus: Automatisierte Justage der Fokussierungsoptiken von
reie-Elektronen-Lasern mit Hilfe von 'machine learning'-Algorithmen (2022-2026)
BMBF-Verbundprojekt 05K2022, Subproject 2 - EXPOWER: EXPOnential analysis emPOWERing innovation (2021-2026)
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)
Teaching
- Lecture: Image and Geometry Processing II (English) (SS 2026)
Monday and Thursday 10.15 - 11.55, MN 67 (Lecture: 4 SWS + Exercises: 2 SWS / 9 ECTS) - Research seminar: Numerical Analysis (English) (SS 2026)
Tuesday 12.30 - 14.00, Seminarraum NAM (2 SWS) - Seminar: Seminar on Applied Fourier Analysis (SS 2026)
Monday 14.15 - 15.45 and Thursday 12:30-14:00, Seminarraum NAM (2 SWS) - Lecture: Image and Geometry Processing I (English) (WS 2025/2026)
Monday and Thursday 10.15 - 11.55, MN 67 (Lecture: 4 SWS + Exercises: 2 SWS / 9 ECTS) - Research seminar: Numerical Analysis (English) (WS 2025/2026)
Tuesday 12.30 - 14.00, Seminarraum NAM (2 SWS) - Seminar: Proseminar über Numerische Approximation (German) (WS 2025/2026)
Monday 14.15 - 15.45, Seminarraum NAM (2 SWS) - Lecture: Numerische Mathematik II (German) (SS 2025)
Tuesday and Friday 10.15 - 11.45, MN 67 (Lecture: 4 SWS / 9 ECTS) - Research seminar: Numerical Analysis (English) (SS 2025)
Tuesday 12.30 - 14.00, MN 55 (2 SWS) - Bachelor Seminar on Numerical Mathematics (German) (SS 2025)
Monday 14:15 - 15:45, MN 55 (2 SWS) - Lecture: Numerische Mathematik I (German) (WS 2024/2025)
Tuesday and Friday 8.15 - 9.45, MN 67 (Lecture: 4 SWS / 9 ECTS) - Research seminar: Numerical Analysis (English) (WS 2024/2025)
Tuesday 12.30 - 14.00 (2 SWS), MN 55 - Lecture: Mathematik für Studierende der Informatik II (German) (SS 2024)
Monday and Thursday 10.15 - 11.45, MN 67 (Lecture: 4 SWS / 9 ECTS) - Research seminar: Numerical Analysis (English) (SS 2024)
Tuesday 12.30 - 14.00 (2 SWS), MN 55
Publications
Preprints
- MOCCA: A Fast Algorithm for Parallel MRI Reconstruction Using Model Based Coil Calibration.
Gerlind Plonka, Yannick Nicola Riebe
University of Göttingen, Institute for Numerical and Applied Mathematics, 2024 (preprint available at arXiv)
2026
- Differential approximation of the Gaussian by short cosine sums with exponential error decay.
Nadiia Derevianko, Gerlind Plonka
Sampl. Theory Signal Process. Data Anal. 24, article number 6, 2026, DOI: 10.1007/s43670-026-00124-9, preprint available at arXiv. - Fast computation of best approximation polynomials for the reciprocal function
Gerlind Plonka, Manfred Tasche
Numerical Algorithms, to appear, 2026, DOI: 10.1007/s11075-026-02364-1. - Image reconstruction from structured subsampled 2D Fourier data
Gerlind Plonka, Anahita Riahi
Journal of Fourier Analysis and Applications 32, article number 16, 2026, (arXiv preprint 22510.18045) , DOI: 10.1007/s00041-025-10230-2.
2025
- Phasebook: A Survey of Selected Open Problems in Phase Retrieval
Marc Allain, Selin Aslan, Wim Coene, Sjoerd Dirksen, Jonathan Dong, Julien Flamant, Mark Iwen, Felix Krahmer, Tristan van Leeuwen, Oleh Melnyk, Andreas Menzel, Allard P. Mosk, Viktor Nikitin, Gerlind Plonka, Palina Salanevich, Matthias Wellershoff
Sampl. Theory Signal Process. Data Anal. 23, 23, 2025, paper online, DOI: 10.1007/s43670-025-00117-0. - Application of deep dictionary learning and predefined filters for classification of retinal optical coherence tomography images.
Zahra Baharlouei, Fariba Shaker, Gerlind Plonka, Hossein Rabbani
IEEE Access 13, 596-607, 2025, paper online, DOI: 10.1109/ACCESS.2024.3522122. - CircWaveDL: Modeling of optical coherence tomography images based on a new supervised tensor-based dictionary learning for classification of macular abnormalities.
Roya Arian, Aliraza Vard, Rahele Kafieh, Gerlind Plonka, Hossein Rabbani
Artificial Intelligence in Medicine 160, 103060 2025, paper online, DOI: 10.1016/j.artmed.2024.103060.
2024
- X-let’s atom combinations for modeling and denoising of OCT images by modified morphological component analysis.
Raha Razavi, Gerlind Plonka, Hossein Rabbani
IEEE Transactions on Medical Imaging 43(2), 760-770, 2024 ( paper online, DOI: 10.1109/TMI.2023.3320977)
2023
- A New Convolutional Neural Network Based on Combination of Circlets and Wavelets for Macular OCT Classification.
Roya Arian, Aliraza Vard, Rahele Kafieh, Gerlind Plonka, Hossein Rabbani
Scientific Reports 13, 22582, 2023 ( open access, DOI: 10.1038/s41598-023-50164-7) - Numerical Fourier Analysis.
Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
Birkhäuser, Basel, 2023 ( book, second edition, 664 pages, Doi: 10.1007/978-3-031-35005-4) - Wavelet scattering transform application in classification of retinal abnormalities using OCT images.
Zahra Baharlouei, Gerlind Plonka, Hossein Rabbani
Scientific Reports 13, 19013, 2023 ( open access, DOI: 10.1038/s41598-023-46200-1) - From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation
Nadiia Derevianko, Gerlind Plonka, Markus Petz
IMA Journal of Numerical Analysis, 43(2), 789–827, 2023 (preprint available at arXiv) - Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models
Gerlind Plonka, Yannick Nicola Riebe, Yurii Kolomoitsev
Analysis and Applications 21(01), 127-163, 2023 (preprint available at arXiv) - ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application.
Nadiia Derevianko, Gerlind Plonka, Raha Razavi
Numerical Algorithms 92, 437-470, 2023 (preprint available at arXiv)
2022
- Combining Non-Data-Adaptive Transforms for OCT Image Denoising by Iterative Basis Pursuit
Raha Razavi, Hossein Rabbani, Gerlind Plonka
2022 IEEE International Conference on Image Processing (ICIP), pp. 2351-2355, 2022 (DOI: 10.1109/ICIP46576.2022.9897319) - Detection of Retinal Abnormalities in OCT Images Using Wavelet Scattering Network
Zahra Baharlouei, Hossein Rabbani, Gerlind Plonka
44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3862-3865, 2022 (DOI: 10.1109/EMBC48229.2022.9871989) - Automatic Classification of Macular Diseases from OCT Images Using CNN Guided with Edge Convolutional Layer
Ebrahim Nasr Esfahani, Parisa Ghaderi Daneshmand, Hossein Rabbani, Gerlind Plonka
44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3858-3861, 2022 (DOI: 10.1109/EMBC48229.2022.9871322) - Reconstruction of Connected Digital Lines Based on Constrained Regularization.
Mojtaba Lashgari, Hossein Rabbani, Gerlind Plonka, Ivan Selesnick
IEEE Transactions on Image Processing 31, 5613-5628, 2022 - Retinal Optical Coherence Tomography image analysis by Restricted Boltzmann Machine.
Mansooreh Ezhet, Gerlind Plonka, Hossein Rabbani
Biomedical Optics Express 13(9), 4539-4558, 2022 - Exact Reconstruction of Extended Exponential Sums Using Rational Approximation of their Fourier Coefficients
Nadiia Derevianko, Gerlind Plonka
Analysis and Applications 20(3), 543-577, 2022 (preprint available at arXiv) - Frame soft shrinkage operators are proximity operators
Jakob Geppert, Gerlind Plonka
Appl. Comput. Harmon. Anal. 57, 185–200, 2022 (preprint available at arXiv)
2021
- Rational Functions for the Reconstruction of Exponential Sums from their Fourier Coefficients
Markus Petz, Gerlind Plonka, Nadiia Derevianko
PAMM · Proc. Appl. Math. Mech. 21:1 e202100078, 2021 (DOI: 10.1002/pamm.202100078) - 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)
2020
- 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)
2019
- 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) - Numerical Fourier Analysis
Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche
Birkhäuser, Basel, 2019 (book, 618 pages) - Sparse Fast DCT for Vectors with One-block Support
Sina Bittens, Gerlind Plonka
Numerical Algorithms 82(2), 663–697, 2019 (preprint as download (arXiv))
2018
- Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
Robert Beinert, Gerlind Plonka
Applied and Computational Harmonic Analysis 45, 505-525, 2018 (preprint as download (arXiv)) - Deterministic sparse FFT for M-sparse vectors
Gerlind Plonka, Katrin Wannenwetsch, Annie Cuyt, Wen-Shin Lee
Numerical Algorithms 78(1), 133-159, 2018 (revised preprint as download) - Sparse graph-regularized dictionary learning for suppressing random seismic noise
Lina Liu, Jianwei Ma, Gerlind Plonka
Geophysics 83(3), pp. V215-V231, 2018 (preprint as download)
2017
- Application of the AAK theory and Prony-like Methods for sparse approximation of exponential sums
Vlada Pototskaia, Gerlind Plonka
Proc. Appl. Math. Mech. Volume 17, pp. 835-836, December 2017 (DOI 10.1002/pamm.20171038) - Sparse phase retrieval of structured signals by Prony’s method
Robert Beinert, Gerlind Plonka
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 829-830, December 2017 (DOI 10.1002/pamm.201710382) - Seismic data interpolation and denoising by learning a tensor tight frame
Lina Liu, Gerlind Plonka, Jianwei Ma
Inverse Problems 33(10), 105011, 2017 (preprint as download) - A sparse Fast Fourier algorithm for real nonnegative vectors
Gerlind Plonka, Katrin Wannenwetsch
Journal of Computational and Applied Mathematics 321, 532-539, 2017 (preprint as download) - Sparse phase retrieval of one-dimensional signals by Prony's method
Robert Beinert, Gerlind Plonka
Frontiers of Applied Mathematics and Statistics 3:5, 2017 (open access, preprint as download)
2016
- Iterative Phase Retrieval with Sparsity Constraints
Stefan Loock, Gerlind Plonka
PAMM 16(1), 835-836, 2016 (DOI: 10.1002/pamm.201610406) - Application of the AAK theory for sparse approximation of exponential sums
Gerlind Plonka, Vlada Pototskaia
working paper, 2016 (preprint as download (arXiv)) - Sparse approximation by Prony's method and AAK theory
Gerlind Plonka, Vlada Pototskaia
Oberwolfach Reports, Volume 33, pp. 16-19, 2016 (preprint as download) - Using sparsity information for iterative phase retrieval in x-ray propagation imaging
Anne Pein, Stefan Loock, Gerlind Plonka, Tim Salditt
Opt. Express 24(8), 8332-8343., 2016 (open access) - Pseudo-inverses of difference matrices and their application to sparse signal approximation
Gerlind Plonka, Sebastian Hoffmann, Joachim Weickert
Linear Algebra and its Applications 503, 26-47, 2016 (preprint as download) - Reconstruction of polygonal shapes from sparse Fourier samples
Marius Wischerhoff, Gerlind Plonka
Journal of Computational and Applied Mathematics 297, 117-131, 2016 (preprint as download) - Relation between total variation and persistence distance and its application in signal processing
Gerlind Plonka, Yi Zheng
Advances in Computational Mathematics 42(3), 651-674, 2016 (preprint (2014) as download) - A deterministic sparse FFT algorithm for vectors with small support
Gerlind Plonka, Katrin Wannenwetsch
Numerical Algorithms 71(4), 889-905, 2016 (preprint as download)
2015
- Deterministic sparse FFT algorithms
Gerlind Plonka, Katrin Wannenwetsch
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 667-668, October 2015 (DOI: 10.1002/pamm.201510323, preprint as download) - Prony's Method for Multivariate Signals
Thomas Peter, Gerlind Plonka, Robert Schaback
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 665-666, October 2015 (DOI: 10.1002/pamm.201510322, preprint as download) - Ambiguities in one-dimensional phase retrieval of structured functions
Robert Beinert, Gerlind Plonka
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 653-654, October 2015 (DOI: 10.1002/pamm.201510316, preprint as download) - A deterministic sparse FFT algorithm for vectors with short support
Gerlind Plonka, Katrin Wannenwetsch
Oberwolfach Reports, Volume 38, pp. 41-44, 2015 - Curvelets
Gerlind Plonka, Jianwei Ma
Encyclopedia of Applied and Computational Mathematics, B. Engquist (eds.), 2015 (pp. 320-321, Springer Berlin, DOI 10.1007/978-3-540-70529-1) - Discrete Green's functions for harmonic and biharmonic inpainting with sparse atoms
Sebastian Hoffmann, Gerlind Plonka, Joachim Weickert
X.-C. Tai et al. (Eds.): Energy Minimization Methods in Computer Vision and Pattern Recognition. LNCS 8932, Springer, Berlin, pp. 169-182, 2015 (preprint as download) - Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes
Robert Beinert, Gerlind Plonka
The Journal of Fourier Analysis and Applications 21(6), 1169-1198, 2015 (preprint as download)
2014
- Phase retrieval for Fresnel measurements using a shearlet sparsity constraint
Stefan Loock, Gerlind Plonka
Inverse Problems 30 (2014) 055005, 2014 (preprint as download) - Prony methods for recovery of structured functions
Gerlind Plonka, M. Tasche
GAMM-Mitt. 37(2), 2014 (239-258, revised preprint as download) - Adaptive approximation algorithms for sparse data representation
M. Guillemard, Dennis Heinen, A. Iske, S. Krause-Solberg, Gerlind Plonka
Lecture Notes in Computational Science and Engineering 102, pp. 281-302, 2014 (preprint as download)
2013
- Optimal representation of piecewise Hölder smooth bivariate functions by the easy path wavelet transform
Gerlind Plonka, Armin Iske, Stefanie Tenorth
Journal of Approximation Theory 176, 2013 (42-67, revised preprint as download) - How many Fourier samples are needed for real function reconstruction?
Gerlind Plonka, Marius Wischerhoff
Journal of Applied Mathematics and Computing, Volume 42, Issue 1-2, pp 117-137, 2013 (revised preprint as download) - A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators
Thomas Peter, Gerlind Plonka
Inverse Problems 29, 2013 (025001, revised preprint as download) - Representation of sparse Legendre expansions
Thomas Peter, Gerlind Plonka, Daniela Rosca
Journal of Symbolic Computation 50, 2013 (159-169, preprint as download)
2012
- Approximation by k-sparse sums of eigenfunctions of linear operators
Thomas Peter, Gerlind Plonka
Oberwolfach Reports 31/2012, 2012 (16-18, pdf as download) - An area preserving projection from the regular octahedron to the sphere
Daniela Rosca, Gerlind Plonka
Results in Mathematics 62(3), 2012 (429-444, open access, preprint as download) - Wavelet shrinkage on paths for denoising of scattered data
Dennis Heinen, Gerlind Plonka
Results in Mathematics 62(3), 2012 (337-354, open access, preprint as download) - Compressive Video Sampling with Approximate Message Passing Decoding
Jianwei Ma, Gerlind Plonka, M. Yousuff Hussaini
IEEE Transactions on Circuits and Systems for Video Technology 22(9), 2012 (1354-1364, revised preprint as download) - Optimally sparse image representation by the easy path wavelet transform
Gerlind Plonka, Stefanie Tenorth, Armin Iske
International Journal of Wavelets, Multiresolution and Information Processing 10(1), 2012 (1250007 (20 pages), revised preprint as download) - Sparse deconvolution methods for ultrasonic NDT
Florian Boßmann, Gerlind Plonka, Thomas Peter, Oliver Nemitz, Till Schmitte
Journal of Nondestructive Evaluation 31(3), 2012 (225-244, open access, revised preprint as download)
2011
- Uniform spherical grids via equal area projection from the cube to the sphere
Daniela Rosca, Gerlind Plonka
Journal of Computational and Applied Mathematics 236, 2011 (1033-1041, preprint as download) - Curvelet-wavelet regularized split Bregman iteration for compressed sensing
Gerlind Plonka, Jianwei Ma
International Journal of Wavelets, Multiresolution and Information Processing 9(1), 2011 (79-110, preprint as download) - A hybrid method for image approximation using the easy path wavelet transform
Gerlind Plonka, Stefanie Tenorth, Daniela Rosca
IEEE Transactions on Image Processing 20(2), 2011 (372-381, preprint as download)
2010
- Easy Path Wavelet Transform on triangulations of the sphere
Gerlind Plonka, Daniela Rosca
Mathematical Geosciences 42(7), 2010 (839-855, preprint as download) - The curvelet transform: A review of recent applications
Jianwei Ma, Gerlind Plonka
IEEE Signal Processing Magazine 27(2), März 2010 (118-133, preprint as download) - A new sparse representation of seismic data using adaptive easy-path wavelet transform
Jianwei Ma, Gerlind Plonka, Hervé Chauris
IEEE Geoscience and Remote Sensing Letters 7(3), 2010 (540-544, preprint as download)
2009
- Image approximation by a hybrid method based on the easy path wavelet transform
Gerlind Plonka, Stefanie Tenorth, Daniela Rosca
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers, 2009 (442-446. (ISBN: 978-1-4244-5825-7)) - A digital diffusion-reaction type filter for nonlinear denoising
Gerlind Plonka
Results in Mathematics 53(3-4), 2009 (371-381, preprint as download) - Sparse data representation on the sphere using the easy path wavelet transform
Gerlind Plonka, Daniela Rosca
Sampling Theory and Applications (SampTA'09), L. Fesquet and B. Torresani (eds.), 2009 (255–258, preprint as download) - Nonlinear locally adaptive wavelet filter banks
Gerlind Plonka, Stefanie Tenorth
Sampling Theory and Applications (SampTA'09), L. Fesquet and B. Torresani (eds.), 2009 (381–384, preprint as download) - Directional Haar wavelet frames on triangles
Jens Krommweh, Gerlind Plonka
Applied and Computational Harmonic Analysis 27, 2009 (215-234, revised preprint as download) - The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data
Gerlind Plonka
Multiscale Modeling and Simulation 7(3), 2009 (1474-1496, revised preprint as download) - Computing with Curvelets: From Image Processing to Turbulent Flows
Jianwei Ma, Gerlind Plonka
Computing in Science and Engineering 11(2), 2009 (72-80, preprint as download)
2008
- Nonlinear regularized reaction-diffusion filters for denoising of images with textures
Gerlind Plonka, Jianwei Ma
IEEE Transactions on Image Processing 17(8), 2008 (1283-1294, preprint as download) - Numerical stability of biorthogonal wavelet transforms
Gerlind Plonka, Hagen Schumacher, Manfred Tasche
Advances in Computational Mathematics 29, 2008 (1-25, preprint as download)
2007
- Combined curvelet shrinkage and nonlinear anisotropic diffusion
Jianwei Ma, Gerlind Plonka
IEEE Transactions on Image Processing 16, 2007 (2198-2206, preprint as download) - Convergence of an iterative nonlinear scheme for denoising of piecewise constant images
Gerlind Plonka, Jianwei Ma
International Journal of Wavelets, Multiresolution and Information Processing 5, 2007 (975-995, preprint as download)
2006
- A multiscale wavelet-inspired scheme for nonlinear diffusion
Gerlind Plonka, Gabriele Steidl
International Journal of Wavelets, Multiresolution and Information Processing 4, 2006 (1-22, preprint as download)
2005
- Fast and numerically stable algorithms for discrete cosine transforms
Gerlind Plonka, Manfred Tasche
Linear Algebra and its Applications 394, 2005 (309-345, preprint as download)
2004
- Numerical stability of fast trigonometric and orthogonal wavelet transforms
Gerlind Plonka, Manfred Tasche
Advences in Constructive Approximation: Vanderbilt (M. Neamtu, E. B. Saff, eds.), Nashboro Press, Brentwood, 2004 (393-419, preprint as download) - A global method for invertible integer DCT and integer wavelet algorithms
Gerlind Plonka
Applied and Computational Harmonic Analysis 16, 2004 (99-110, preprint as download)
2003
- Properties of locally linearly independent function vectors
Gerlind Plonka, Ding-Xuan Zhou
Journal of Approximation Theory 122, 2003 (24-41, preprint as download) - Integer DCT-II by lifting steps
Gerlind Plonka, Manfred Tasche
International Series of Numerical Mathematics (W. Haussmann, K. Jetter, M. Reimer, J. Stöckler (eds.)), Vol. 145, Birkhäuser, Basel, 2003 (235-252, preprint as download) - Invertible integer DCT algorithms
Gerlind Plonka, Manfred Tasche
Applied and Computational Harmonic Analysis 15, 2003 (70-88, preprint as download)
2002
- How many holes can locally linearly independent refinable function vectors have?
Gerlind Plonka
Algorithms for Approximation IV, Proceedings of the 2001 International Symposium (J. Levesley, I. J. Anderson, J. C. Mason, eds.), The University of Huddersfield, 2002 (378-393, preprint as download) - Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks
Di-Rong Chen, Gerlind Plonka
Journal of Approximation Theory 119, 2002 (133-155, preprint as download)
2001
- A survey on L2-Approximation order from shift-invariant spaces
Kurt Jetter, Gerlind Plonka
Multivariate Approximation and Applications (N. Dyn, D. Leviatan, D. Levin, A. Pinkus, eds.), Cambridge University Press, 2001 (73-111, preprint as download) - A new factorization technique for the matrix mask of univariate refinable functions
Gerlind Plonka, Amos Ron
Numerische Mathematik 87, 2001 (555-595, preprint as download)
2000
- Some notes on two-scale difference equations
Lothar Berg, Gerlind Plonka
Functional Equations and Inequalities (T.M. Rassias, ed.), Kluwer Academic Publishers, 2000 (7-29, preprint as download)
1999
- Spectral properties of two-slanted matrices
Lothar Berg, Gerlind Plonka
Results in Mathematics 35, 1999 (201-215, preprint as download)
1998
- Compactly supported solutions of two-scale difference equations
Lothar Berg, Gerlind Plonka
Linear Algebra and its Applications 275, 1998 (49-75, preprint as download) - Construction of multi-scaling functions with approximation and symmetry
Gerlind Plonka, Vasily Strela
SIAM Journal on Mathematical Analysis 29, 1998 (481-510, preprint as download) - From wavelets to multiwavelets
Gerlind Plonka, Vasily Strela
Mathematical Methods of Curves and Surfaces II (M. Daehlen, T. Lyche and L. L. Schumaker, eds.), Vanderbilt University Press, Nashville, 1998 (1-25, preprint as download)
1997
- Refinement of vectors of Bernstein polynomials
Lothar Berg, Gerlind Plonka
Rostocker Mathematisches Kolloquium 50, 1997 (19-30, preprint as download) - Stability of translates of scaling vectors
Gerlind Plonka
Computational Mathematics (Achim Sydow, ed.), Wissenschaft und Technik Verlag, Berlin, 1997 (293-300) - On stability of scaling vectors
Gerlind Plonka
Surface Fitting and Multiresolution Methods (A. Le Mehauté, C. Rabut, L. L. Schumaker, eds.), Vanderbilt University Press, Nashville, 1997 (293-300, preprint as download) - Necessary and sufficient conditions for orthonormality of scaling vectors
Gerlind Plonka
Multivariate Approximation and Splines (G. Nürnberger, J. W. Schmidt, G. Walz, eds.), ISNM Vol: 125, Birkhäuser, Basel, 1997 (205-218, preprint as download) - Regularity of refinable function vectors
Albert Cohen, Ingrid Daubechies, Gerlind Plonka
Journal of Fourier Analysis and Applications 3, 1997 (295-324, preprint as download) - Approximation order provided by refinable function vectors
Gerlind Plonka
Constructive Approximation 13, 1997 (221-244, preprint as download)
1996
- Generalized spline wavelets
Gerlind Plonka
Constructive Approximation 12, 1996 (127-155, preprint as download)
1995
- Approximation properties of multi-scaling functions: A Fourier approach
Gerlind Plonka
Rostocker Mathematisches Kolloquium 49, 1995 (115-126, preprint as download) - Factorization of refinement masks of function vectors
Gerlind Plonka
Wavelets and Multilevel Approximation (C. K. Chui, L. L. Schumaker, eds.), Singapore: World Scientific Publishing Co., 1995 (317-324, preprint as download) - On the construction of wavelets on a bounded interval
Gerlind Plonka, Kathi Selig, Manfred Tasche
Advances in Computational Mathematics 4, 1995 (357-388, preprint as download) - On the computation of periodic spline wavelets
Gerlind Plonka
Applied and Computional Harmonic Analysis 2, 1995 (1-22)
1994
- Two-scale symbol and autocorrelation symbol for B-splines with multiple knots
Gerlind Plonka
Advances in Computational Mathematics 3, 1994 (387-398) - A unified approach to periodic wavelets
Gerlind Plonka, Manfred Tasche
C. K. Chui, L. Montefusco u. L. Puccio (Eds.). Wavelets: Theory, Algorithms and Applications. Boston: Academic Press, 1994 (137-151) - Spline wavelets with higher defect
Gerlind Plonka
P. J. Laurent, A. Le Mehauté u. L. L. Schumaker (Eds.). Wavelets, Images and Surface Fitting. Boston: AKPeters, 1994 (387-398) - Cardinal Hermite spline interpolation with shifted nodes
Gerlind Plonka, Manfred Tasche
Mathematics of Computation 63, 1994 (645-659) - Optimal shift parameters for periodic spline interpolation
Gerlind Plonka
Numerical Algorithms 6, 1994 (297-316) - Periodic spline interpolation with shifted nodes
Gerlind Plonka
Journal of Appoximation Theory 76, 1994 (1-20)
1993
- An efficient algorithm for periodic Hermite spline interpolation with shifted nodes
Gerlind Plonka
Numerical Algorithms 5, 1993 (51-62) - Nonperiodic Hermite spline interpolation
Gerlind Plonka
Rostocker Mathematisches Kolloquium 46, 1993 (65-74)
1992
- Efficient algorithms for the periodic Hermite spline interpolation
Gerlind Plonka, Manfred Tasche
Mathematics of Computation 58, 1992 (693-703)
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 - Reconstruction of Sparse Non-Harmonic Signals
Exact Reconstruction of Sparse Non-Harmonic Signals from Fourier Coefficients, implemented in MATLAB.
Markus Petz, Gerlind Plonka, Nadiia Derevianko - Reconstruction of Extended Exponential Sums
Exact Reconstruction of Extended Exponential Sums using Rational Approximation of their Fourier Coefficients, implemented in MATLAB.
Nadiia Derevianko, Gerlind Plonka - From ESPRIT to ESPIRA
From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation, implemented in MATLAB.
Nadiia Derevianko, Gerlind Plonka, Markus Petz - MOCCA-MRI
MOCCA: A Fast Algorithm for Parallel MRI Reconstruction Using Model Based Coil Calibration, implemented in MATLAB.
Gerlind Plonka, Yannick Nicola Riebe - 2D Subsampled Fourier Reconstruction
Image reconstruction from structured subsampled 2D Fourier data, implemented in MATLAB.
Gerlind Plonka, Anahita Riahi