Publications

Preprints:

• Image reconstruction from structured subsampled 2D Fourier data
  Gerlind Plonka, Anahita Riahi
  University of Göttingen, Institute for Numerical and Applied Mathematics, 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, preprint 2025.
• 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.
• Differential approximation of the Gaussian by short cosine sums with exponential error decay.
  Nadiia Derevianko, Gerlind Plonka
  University of Göttingen, Institute for Numerical and Applied Mathematics, 2023, preprint available at arXiv.
• Adaptive sampling recovery of functions with higher mixed regularity
  Nadiia Derevianko, Tino Ullrich
  University of Göttingen, Institute for Numerical and Applied Mathematics, 2020, preprint available at arXiv.

2025:

• 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.
• Sharp Lp-error estimates for sampling operators
  Yurii Kolomoitsev, Tetiana Lomako
  J. Approx. Theory, Available online 26 June 2023, 105941, 2023, preprint available at arXiv.
• 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.
• On generalized K-functionals in Lp for 0 < p < 1
  Yurii Kolomoitsev, Tetiana Lomako
  Fract. Calc. Appl. Anal. 26, 1016–1030, 2023, preprint available at arXiv.
• Sparse grid approximation in weighted Wiener spaces
  Yurii Kolomoitsev, Tetiana Lomako, Sergey Tikhonov
  J. Fourier Anal. Appl. 29, 19, 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,
• Uniform approximation by multivariate quasi-projection operators
  Yurii Kolomoitsev, Maria Skopina
  Anal. Math. Phys. 12, no. 2, Paper No. 68, 2022, preprint available at arXiv.
• Approximation by quasi-interpolation operators and Smolyak's algorithm
  Yurii Kolomoitsev
  J. of Complexity 69, 101601, 2022, preprint available at arXiv.
• 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:

• Optimal rank-1 Hankel approximation in the spectral norm for matrices with multiple largest eigenvalue
  Hanna Knirsch
  PAMM · Proc. Appl. Math. Mech. 21:1 e202100012, 2021, DOI: 10.1002/pamm.202100012.
• 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.
• Approximation properties of periodic multivariate quasi-interpolation operators
  Yurii Kolomoitsev, Jürgen Prestin
  J. Approx. Theory 270, 105631, 2021, preprint available at arXiv.
• Asymptotics of the Lebesgue constants for bivariate approximation processes
  Yurii Kolomoitsev, Tetiana Lomako
  Appl. Math. Comput. 403, 126192, 2021, preprint available at arXiv.
• Hardy-Littlewood and Ulyanov inequalities
  Yurii Kolomoitsev, Sergey Tikhonov
  Mem. Amer. Math. Soc. 271, no. 1325, 2021, preprint available at arXiv.
• Asymptotics of the Lebesgue constants for a d-dimensional simplex
  Yurii Kolomoitsev, Elijah Liflyand
  Proc. Amer. Math. Soc. 149, 2911-2926, 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.
• Quasi-projection operators in the weighted Lp spaces
  Yurii Kolomoitsev, Maria Skopina
  Appl. Comput. Harmon. Anal. 52, 165-197, 2021, preprint available at arXiv.
• 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.
• Approximation by multivariate quasi-projection operators and Fourier multipliers
  Yurii Kolomoitsev, Maria Skopina
  Appl. Math. Comput. 400, 125955, 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:

• Smoothness of functions vs. smoothness of approximation processes
  Yurii Kolomoitsev, Sergey Tikhonov
  Bull. Math. Sci. 10, no. 3, 2030002, 2020, preprint available at arXiv.
• 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.
• Approximation by periodic multivariate quasi-projection operators
  Yurii Kolomoitsev, Aleksandr Krivoshein, Maria Skopina
  J. Math. Anal. Appl. 489, no. 2, 124192, 2020, preprint available at arXiv.
• Properties of moduli of smoothness in Lp(Rd)
  Yurii Kolomoitsev, Sergey Tikhonov
  J. Approx. Theory 257, 105423, 2020, preprint available at arXiv.
• Approximation of Gaussians by spherical Gauss-Laguerre basis in the weighted Hilbert space
  Nadiia Derevianko, Jürgen Prestin
  Electron. Trans. Numer. Anal. 52, 249-269, 2020, preprint available as pdf.
• On higher order Faber spline basis for sampling discretization of functions
  Nadiia Derevianko, Tino Ullrich
  J. Approx. Theory, 257, 105449, 2020, preprint available at arXiv.
• Approximation by sampling-type operators in Lp-spaces
  Yurii Kolomoitsev, Maria Skopina
  Math. Methods Appl. Sciences 43, no. 16, 9358-9374, 2020, preprint available at arXiv.
• 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.

2019:

• 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.
• On an orthogonal bivariate trigonometric Schauder basis for the space of continuous functions
  Nadiia Derevianko, Vitalii Myroniuk, Jürgen Prestin
  J. Approx. Theory, V. 238, pp. 67-84, 2019, preprint as download.
• Computation of adaptive Fourier series bysparse 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).
• Sparse Fast Trigonometric Transforms
  Sina Bittens
  Dissertation, 2019, published online on 22 July 2019, http://hdl.handle.net/21.11130/00-1735-0000-0003-C16D-9.
• A deterministic sparse FFT for functions with structured Fourier sparsity
  Sina Bittens, Ruochuan Zhang, Mark Iwen
  Advances in Computational Mathematics, 45(2), pp. 519-561, 2019, https://doi.org/10.1007/s10444-018-9626-4, preprint as download.
• 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.
• Sparse Power Factorization: Balancing peakiness and sample complexity
  Dominik Stöger, Jakob Geppert, Felix Krahmer
  Advances in Computational Mathematics 45(3), 1711--1728, 2019, preprint available at arXiv.
• 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:

• Sparse Power Factorization With Refined Peakiness Conditions
  Dominik Stöger, Jakob Geppert, Felix Krahmer
  2018 IEEE Statistical Signal Processing Workshop (SSP), 2018, See at IEEE Xplore.
• 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:

• Image Compression with the Region Based Easy Path Wavelet Transform
  Renato Budinich
  Proc. Appl. Math. Mech. Volume 17, pp. 831-832, December 2017, DOI 10.1002/pamm.201710383.
• 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.
• Application of AAK theory for sparse approximation
  Vlada Pototskaia
  Dissertation, 2017, published online on 27 October 2017, http://hdl.handle.net/11858/00-1735-0000-0023-3F4B-1.
• A region based easy path wavelet transform for sparse image representation
  Renato Budinich
  International Journal of Wavelets, Multiresolution and Information Processing 15, 1750045 (2017) [23 pages], 2017, preprint as download.
• Refined performance guarantees for Sparse Power Factorization
  Jakob Geppert, Felix Krahmer, Dominik Stöger
  2017 International Conference on Sampling Theory and Applications (SampTA), 2017, See at IEEE Xplore.
• 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.
• Characterization of local Besov spaces via wavelet basis expansions
  Nadiia Derevianko, Vitalii Myroniuk, Jürgen Prestin
  Front. Appl. Math. Stat. 3:4. doi: 10.3389/fams.2017.00004, 2017, preprint available as pdf.
• One-dimensional phase retrieval with additional interference measurements
  Robert Beinert
  Results Math. 72(1-2) (2017), 1–24, 2017, preprint as download (arXiv).
• Non-negativity constraints in the one-dimensional discrete-time phase retrieval problem
  Robert Beinert
  Information and Inference: A Journal of the IMA 6, 213-224, 2017, preprint as download (arXiv).
• 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.
• Ambiguities in one-dimensional phase retrieval from magnitudes of a linear canonical transform
  Robert Beinert
  Z. Angew. Math. Mech. (ZAMM), 1–5, 2017, preprint as download (arXiv).
• Sparse FFT for Functions with Short Frequency Support
  Sina Bittens
  Dolomites Research Notes on Approximation 10, pp. 43--55, 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.
• Deterministic Sparse FFT Algorithms
  Katrin Wannenwetsch
  Dissertation, 2016, published online on 30 September 2016, http://hdl.handle.net/11858/00-1735-0000-002B-7C10-0.
• 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.
• Phase Retrieval with Sparsity Constraints
  Stefan Loock
  Dissertation, 2016, published online on 29 June 2016.
• Asymmetric chirplet transform II: phase, frequency, and chirp rate
  Florian Boßmann, Jianwei Ma
  Geophysics 81(6), V425-V439, 2016, link.
• 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.
• Ambiguities in one-dimensional phase retrieval from Fourier magnitudes
  Robert Beinert
  Dissertation, 2015, published online on 13 January 2016, http://hdl.handle.net/11858/00-1735-0000-0028-8691-3.
• 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:

• Fast Subspace Approximation via Greedy Least-Squares
  M. Iwen, Felix Krahmer
  Constructive Approximation 42(2), 281-301, 2015, preprint as download.
• Asymmetric chirplet transform for sparsity representation of seismic data
  Florian Boßmann, Jianwei Ma
  Geophysics 80(6), WD89-WD100, 2015, preprint as download, DOI: 10.1190/geo2015-0063.1.
• 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 Partial Derandomization of PhaseLift using Spherical Designs
  D. Gross, Felix Krahmer, R. Küng
  J. Fourier Anal. Appl. 21(2), 229-266, 2015, preprint as download.
• Linear Widths of the Classes S^Ω_{p,θ}B of Periodic Functions of Many Variables
  Nadiia Derevianko, O.I. Cheremshyns’ka
  Zb. Pr. Inst. Mat. NAN Ukr. 12, No. 4, 165-185 (in Ukrainian), 2015, 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,
• Application of persistent homology in signal and image denoising
  Yi Zheng
  Dissertation, 2015, published online on 29 July 2015, http://hdl.handle.net/11858/00-1735-0000-001C-7131-B.
• Computing and Analyzing Recoverable Supports for Sparse Reconstruction
  Christian Kruschel, D.A. Lorenz
  Advances in Computational Mathematics 41(6), pp. 1119-1144, 2015, early version: ArXiv.
• Reconstruction of Structured Functions from Sparse Fourier Data
  Marius Wischerhoff
  Dissertation, 2014, published online on 19 January 2015, http://hdl.handle.net/11858/00-1735-0000-001C-7131-B.
• Testable uniqueness conditions for empirical assessment of undersampling levels in total variation-regularized x-ray CT
  J.S. Jørgensen, Christian Kruschel, D.A. Lorenz
  Inverse Problems in Science and Engineering 23(8), 2015, pp. 1283-1305, open access.
• 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.
• An RIP approach to Sigma-Delta quantization for compressed sensing
  Joe-Mei Feng, Felix Krahmer
  IEEE Signal Process. Lett. 21(11), 1351-1355, 2014, preprint as download.
• Estimations of Linear Widths of the Classes B^Ω_{p,θ} of Periodic Functions of Many Variables in the Space L_q
  Nadiia Derevianko
  Ukr. Math. J. 66, No. 7, 1013-1027, 2014, preprint as download.
• Approximation of the Classes H^Ω_p of Periodic Functions of Many Variables in the Space L_p
  Nadiia Derevianko
  Ukr. Math. J. 66, No. 5, 707-718, 2014, preprint as download.
• Estimates of Linear Widths of the Classes H^Ω_p of Periodic Functions of Many Variables in the Space L_q
  Nadiia Derevianko
  Zb. Pr. Inst. Mat. NAN Ukr. 11, No. 3, 128 - 145 (in Ukrainian), 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.
• Sparse Matrices in Frame Theory
  Felix Krahmer, G. Kutyniok, J. Lemvig
  Computational Statistics 29, 547-568, 2014, preprint as download.
• Suprema of Chaos Processes and the Restricted Isometry Property
  Felix Krahmer, S. Mendelson, H. Rauhut
  Comm. Pure Appl. Math. 67(11), 1877-1904, 2014, preprint as download.
• Sigma-Delta quantization of sub-Gaussian frame expansions and its application to compressed sensing
  Felix Krahmer, R. Saab, Ö. Yilmaz
  Inform. Inference 3(1), 40-58, 2014, preprint as download.
• Local sampling and approximation of operators with bandlimited Kohn-Nirenberg symbols
  Felix Krahmer, G. Pfander
  Constr. Approx. 39(3), 541-572, 2014, preprint as download.
• Stable and robust sampling strategies for compressive imaging
  Felix Krahmer, R. Ward
  IEEE Trans. Image Proc. 23(2): 612-622, 2014, preprint as download.

2013:

• Generalized Prony Method
  Thomas Peter
  Dissertation, 2013, published in Der Andere Verlag, 2014.
• Model Based Defect Reconstruction in Ultrasonic Non-Destructive Testing
  Florian Boßmann
  Dissertation, October 2013, ISBN: 978-3-86247-450-9, Der Andere Verlag.
• Methoden zur Bildrekonstruktion aus unvollständigen Mengen von Waveletkoeffizienten
  Vlada Pototskaia
  University of Göttingen, September 2013, Master thesis, supervisor: Frau Prof. Dr. Plonka-Hoch.
• Estimates of the Ortho-projective Widths of Classes B^Ω_{p,θ} of Periodic Functions of Many Variables in the Space L_q
  Nadiia Derevianko
  Zb. Pr. Inst. Mat. NAN Ukr. 10, No. 1, 95-109 (in Ukrainian), 2013, preprint as download.
• Trigonometric Widths of Classes of Periodic Functions of Many Variables
  Nadiia Derevianko
  Ukr. Math. J. 64, No. 8, 1185-1198, 2013, preprint as download.
• Real function reconstruction from sparse Fourier samples
  Marius Wischerhoff
  Proc. Appl. Math. Mech. Volume 13, Issue 1, pp. 491–492, 2013, preprint as download.
• Multilevel Gauß-Newton Methoden zur Phasenrekonstruktion
  Robert Beinert
  University of Göttingen, March 2013, Master thesis, supervisor: Frau Prof. Dr. Plonka-Hoch.
• 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.
• Sparsity and spectral properties of dual frames
  Felix Krahmer, G. Kutyniok, J. Lemvig
  Linear Algebra and its Applications 439(4), 2013, 982-998, 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:

• Ortho-projective Widths of Classes of Periodic Functions of Many Variables
  Nadiia Derevianko
  Zb. Pr. Inst. Mat. NAN Ukr. 9, No. 2, 146-156 (in Ukranian), 2012, preprint as download.
• 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.
• Lower bounds for the error decay incurred by coarse quantization schemes
  Felix Krahmer, Rachel Ward
  Appl. Comput. Harmonic Anal. 32(1), 2012, 131-138, preprint as download.
• Root-exponential accuracy for coarse quantization of finite frame expansions
  Felix Krahmer, R. Saab, Rachel Ward
  IEEE J. Inf. Theo. 58(2), 2012, 1069-1079, preprint as download.
• SqFreeEVAL: An (almost) optimal real-root isolation algorithm
  M. Burr, Felix Krahmer
  Journal of Symbolic Computation 47(2), 2012, 153-166, 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:

• Master's thesis: Modeling and Analysis of Calibrating Cone-Beam-CT
  Christian Kruschel
  TU Braunschweig, Institut for Analysis and Algebra, June 2011, Supervisor: Prof. Dr. Dirk Lorenz, In cooperation with SIEMENS Healthcare, Forchheim.
• An Optimal Family of Exponentially Accurate One-Bit Sigma-Delta Quantization Schemes
  Percy Deift, C. Sinan Güntürk, Felix Krahmer
  Comm. Pure Appl. Math. 64(7), 2011, 883-919, preprint as download.
• New and improved Johnson-Lindenstrauss embeddings via the Restricted Isometry Property
  Felix Krahmer, Rachel Ward
  SIAM J. Math. Anal. 43(3), 2011, 1269-1281, preprint as download.
• Optimally sparse frames
  Peter Casazza, P. Heinecke, Felix Krahmer, Gitta Kutyniok
  IEEE J. Inf. Theo. 57(11), 2011, 7279-7287, preprint as download.
• 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.
• Adaptive Waveletmethoden zur Approximation von Bildern
  Stefanie Tenorth
  Universität Göttingen, Juli 2011, Dissertation.
• Nonlinear approximation by sums of exponentials and translates
  Thomas Peter, Daniel Potts, Manfred Tasche
  SIAM J. Sci. Comput. 33(4), 2011, 1920-1947, 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:

• Behandlung von Poisson- und Gamma-Störungen in digitalen Bildern mit Hilfe von Splitting-Methoden
  Marius Wischerhoff
  Universität Duisburg-Essen, Fachbereich Mathematik, Juli 2010, Diplomarbeit, Betreuerin: Frau Prof. Dr. Plonka-Hoch.
• Easy Path Wavelet Transform on triangulations of the sphere
  Gerlind Plonka, Daniela Rosca
  Mathematical Geosciences 42(7), 2010, 839-855, preprint as download.
• Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation
  Jens Krommweh
  Journal of Visual Communication and Image Representation 21(4), 2010, 364-374, preprint as download.
• Tetrolet shrinkage with anisotropic total variation minimization for image approximation
  Jens Krommweh, Jianwei Ma
  Signal Processing 90(8), 2010, 2529-2539, 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.
• Bildapproximation mittels Wedgelets
  Dennis Heinen
  Universität Duisburg-Essen, Fachbereich Mathematik, März 2010, Diploma thesis, supervisor: Prof. Dr. Plonka-Hoch.
• 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).
• Parameterbestimmung bei anharmonischen Fouriersummen mittels approximativer Prony-Methode
  Thomas Peter
  Universität Rostock, Institut für Mathematik, Oktober 2009, Diplomarbeit, Betreuer: Prof. Dr. Manfred Tasche.
• Nonlinear and adaptive frame approximation schemes for elliptic PDEs: Theory and Numerical Experiments
  Stephan Dahlke, Massimo Fornasier, Miriam Primbs, Thorsten Raasch, Manuel Werner
  Numerical Methods for Partial Differential Equations 25(6), 2009, 1261–1510.
• New stable biorthogonal spline-wavelets on the interval
  Miriam Primbs
  Results in Mathematics 57(1-2), 2009, 121-162.
• Entwicklung einer automatisierten Auswertung von bildgebenden Ultraschallverfahren
  Florian Boßmann
  Universität Duisburg-Essen, Fachbereich Mathematik, Oktober 2009, Diploma thesis, supervisor: Prof. Dr. Plonka-Hoch.
• A digital diffusion-reaction type filter for nonlinear denoising
  Gerlind Plonka
  Results in Mathematics 53(3-4), 2009, 371-381, preprint as download.
• An orthonormal basis of directional Haar wavelets on triangles
  Jens Krommweh
  Results in Mathematics 53(3-4), 2009, 323-331, preprint as download.
• The method of stable completion in the classical wavelet context
  Miriam Primbs
  Results in Mathematics 53(3-4), 2009, 391-398.
• Tight frame characterization of multiwavelet vector functions in terms of the polyphase matrix
  Jens Krommweh
  International Journal of Wavelets, Multiresolution and Information Processing 7(1), 2009, 9-21, 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.
• Image approximation by adaptive tetrolet transform
  Jens Krommweh
  Sampling Theory and Applications (SampTA'09), L. Fesquet and B. Torresani (eds.), 2009, 81–84, preprint as download.
• Novel Schemes for Sigma-Delta Modulation: Improved Exponential Accuracy to Low-Complexity Design
  Felix Krahmer
  New York University, 2009, PhD thesis.
• 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:

• Uncertainty in time-frequency representations on finite abelian groups and applications
  Felix Krahmer, Götz E. Pfander, Peter Rashkov
  Appl. Comput. Harmon. Anal. 25(2), 2008, 209-225, preprint as download.
• 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.
• Verallgemeinerte Rudin-Osher-Fatemi-Regularisierung zur Signalentstörung
  Stefanie Tenorth
  Universität Duisburg-Essen, Fachbereich Mathematik, Januar 2008, Diploma thesis, supervisor: Prof. Dr. Plonka-Hoch.
• On the computation of Gramian matrices for refinable bases on the interval
  Miriam Primbs
  International Journal of Wavelets, Multiresolution and Information Processing 6(3), 2008, 459-479.

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.
• Worst-case error analysis of lifting-based fast DCT-algorithms
  Miriam Primbs
  IEEE Transactions on Signal Processing 53(8), 2005, 3211-3218, 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.