Prof. Dr. Gerlind Plonka

University of Göttingen, Institute for Numerical and Applied Mathematics

February 10, 2024

Book:

[1]  Gerlind Plonka, Daniel Potts, Gabriele Steidl, and Manfred Tasche

Numerical Fourier Analysis.
ANHA, Birkhäuser, second edition, ISBN 978-3-031-35004-7, 2023.

[2]  Gerlind Plonka, Daniel Potts, Gabriele Steidl, and Manfred Tasche

Numerical Fourier Analysis.
ANHA, Birkhäuser, ISBN 978-3-030-04305-6, 2019.

Peer-reviewed publications:

[103]  Raha Razavi, Gerlind Plonka, and Hossein Rabbani.

X-let’s atom combinations for modeling and denoising of OCT images by modified morphological component analysis.
IEEE Transactions on Medical Imaging 43(2), 760-770 (2024), doi: 10.1109/TMI.2023.3320977.

[102]  Roya Arian, Alireza Vard, Rahele Kafieh, Gerlind Plonka, and Hossein Rabbani.

A new convolutional neural network based on combination of circlets and wavelets for macular OCT classification.
Scientific Reports 13, 22582 (2023).

[101]  Zahra Baharlouei, Hossein Rabbani, and Gerlind Plonka.

Wavelet scattering transform application in classification of retinal abnormalities using OCT images.
Scientific Reports 13, 19013 (2023).

[100]  Nadiia Derevianko, Gerlind Plonka, and Markus Petz

From ESPRIT to ESPIRA: Estimation of Signal Parameters by Iterative Rational Approximation.
IMA Journal of Numerical Analysis 43(2), 789–827 (2023) (arXiv preprint#2106.15140)

[99]  Gerlind Plonka, Yannick Riebe, and Yurii Kolomoitsev.

Spline Representation and Redundancies of One-Dimensional ReLU Neural Network Models.
Analysis and Applications 21(01), 127-163 (2023) (arXiv preprint#2207.14609)

[98]  Nadiia Derevianko, Gerlind Plonka, and Raha Razavi.

ESPRIT versus ESPIRA for reconstruction of short cosine sums and its application.
Numerical Algorithms 92, 437-470 (2023).
(arXiv preprint#2204.03312)

[97]  Raha Razavi, Hossein Rabbani, and Gerlind Plonka.

Combining Non-Data-Adaptive Transforms for OCT Image Denoising by Iterative Basis Pursuit.
2022 IEEE International Conference on Image Processing (ICIP), pp. 2351-2355, 2022, DOI: 10.1109/ICIP46576.2022.9897319.

[96]  Mojtaba Lashgari, Hossein Rabbani, Gerlind Plonka, and Ivan Selesnick.

Reconstruction of Connected Digital Lines Based on Constrained Regularization.
IEEE Transactions on Image Processing 31, 5613-5628 (2022).

[95]  Ebrahim Nasr Esfahani, Parisa Ghaderi Daneshmand, Gerlind Plonka, and Hossein Rabbani.

Automatic classification of macular deseases from OCT images using CNN guided with edge convolutional layer.
44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3858-3861 (2022), DOI: 10.1109/EMBC48229.2022.9871322.

[94]  Zahra Baharlouei, Gerlind Plonka, and Hossein Rabbani.

Detection of retinal abnormalities in OCT images using wavelet scattering network.
44th Annual International Conference of the IEEE Engineering in Medicine & Biology Society (EMBC), pp. 3862-3865, 2022, DOI: 10.1109/EMBC48229.2022.9871989.

[93]  Mansooreh Ezhet, Gerlind Plonka, and Hossein Rabbani.

Retinal Optical Coherence Tomography Image Analysis by Restricted Boltzmann Machine.
Biomedical Optics Express, 13(9), 4539-4558 (2022).

[92]  Jakob Alexander Geppert and Gerlind Plonka

Frame soft shrinkage operators are proximity operators.
Applied and Computational Harmonic Analyis 57, 185–200 (2022).
Download PDF (preprint)

[91]  Nadiia Derevianko and Gerlind Plonka

Exact Reconstruction of Extended Exponential Sums Using Rational Approximation of their Fourier Coefficients.
Analysis and Applications 20(3), 543-577 (2022), open access.
(arXiv preprint#2103.07743)

[90]  Sahar Jordani, Zahra Amini, Gerlind Plonka, and Hossein Rabbani

Statistical modeling of retinal optical coherence tomography using the Weibull mixture model.
Biomedical Optics Express 12(9), 5470-5488 (2021), open access.

[89]  Hanna Knirsch, Markus Petz, and Gerlind Plonka

Optimal Rank-1 Hankel Approximation of Matrices: Frobenius Norm and Spectral Norm and Cadzow's Algorithm.
Linear Algebra and its Applications 629, 1-39 (2021). (arXiv preprint#2004.11099)

[88]  Markus Petz, Gerlind Plonka, and Nadiia Derevianko

Exact Reconstruction of Sparse Non-Harmonic Signals from their Fourier Coefficients.
Sampling Theory, Signal Processing, and Data Analysis 19, 7 (2021), open access.
(arXiv preprint#2011.13346)

[87]  Gerlind Plonka and Therese von Wulffen

Deterministic sparse sublinear FFT with improved numerical stability.
Results Math. 76(2), 53 (2021).
(arXiv preprint#2004.11097)

[86]  Ingeborg Keller and Gerlind Plonka

Modifications of Prony's method for the recovery and sparse approximation of generalized exponential sums.
In: Fasshauer G.E., Neamtu M., Schumaker L.L. (eds) Approximation Theory XVI. AT 2019.
Springer Proceedings in Mathematics & Statistics, 2021, vol 336, Springer, Cham.
Doi: 10.1007/978-3-030-57464-2_7
Download PDF (arXiv preprint#2001.03651)

[85]  M. Hasannasab, J. Hertrich, S. Neumayer, G. Plonka, S. Setzer, G. Steidl

Parseval proximal neural networks.
Fourier Anal. Appl. 26, 59 (2020). Doi: 10.1007/s00041-020-09761-7
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[84]  Renato Budinich and Gerlind Plonka

A tree-based dictionary learning framework.
International Journal of Wavelets, Multiresolution and Information Processing (2020) 2050041
(24 pages).
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[83]  Robert Beinert and Gerlind Plonka

One-Dimensional Discrete-Time Phase Retrieval.
in: Nanoscale Photonic Imaging (T. Salditt et al., eds.), Topics in Applied Physics 134 (2020), 603-627.
Chapter 24.
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[82]  Kilian Stampfer and Gerlind Plonka

The generalized operator-based Prony method.
Constructive Approximation 52 (2020), 247-282. (online).
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[81]  Sina Bittens and Gerlind Plonka

Real Sparse Fast DCT for Vectors with Short Support.
Linear Algebra and its Applications 582 (2019), 359-390.
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[80]  Sina Bittens and Gerlind Plonka

Sparse Fast DCT for Vectors with One-block Support.
Numerical Algorithms 82(2) (2019), 663-697.
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[79]  Gerlind Plonka and Vlada Pototskaia

Computation of adaptive Fourier series by sparse approximation of exponential sums.
Journal of Fourier Analysis and Applications 25(4) (2019), 1580–1608.
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[78]  Ran Zhang and Gerlind Plonka

Optimal approximation with exponential sums by maximum likelihood modification of Prony's method.
Advances in Computational Mathematics 45(3) (2019), 1657-1687.
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[77]  Gerlind Plonka, Kilian Stampfer and Ingeborg Keller

Reconstruction of stationary and non-stationary signals by the generalized Prony method.
Analysis and Applications 17(2) (2019), 179-210.
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[76]  Robert Beinert and Gerlind Plonka

Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain.
Applied and Computational Harmonic Analysis 45 (2018), 505-525.
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[75]  Lina Liu, Jianwei Ma, and Gerlind Plonka

Sparse graph-regularized dictionary learning for suppressing random seismic noise.
Geophysics 83(3) (2018), V215-V231.
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[74]  Gerlind Plonka, Katrin Wannenwetsch, Annie Cuyt, and Wen-Shin Lee

Deterministic sparse FFT for M-sparse vectors.
Numerical Algorithms 78(1) (2018), 133-159.
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[73]  Lina Liu, Gerlind Plonka, and Jianwei Ma

Seismic data interpolation and denoising by learning a tensor tight frame.
Inverse Problems 33(10) (2017), 105011.
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[72]  Robert Beinert and Gerlind Plonka

Sparse phase retrieval of one-dimensional signals by Prony's method.
Frontiers of Applied Mathematics and Statistics 3:5 (2017), open access, doi: 10.3389/fams.2017.00005.
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[71]  Gerlind Plonka and Katrin Wannenwetsch

A sparse Fast Fourier algorithm for real nonnegative vectors.
Journal of Computational and Applied Mathematics 321 (2017), 532-539.
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[70]  Anne Pein, Stefan Loock, Gerlind Plonka, and Tim Salditt

Using sparsity information for iterative phase retrieval in x-ray propagation imaging
Opt. Express 24(8) (2016), 8332-8343.
open access

[69]  Gerlind Plonka, Sebastian Hoffmann, Joachim Weickert

Pseudo-inverses of difference matrices and their application to sparse signal approximation.
Linear Algebra and its Applications 503 (2016), 26-47.
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[68]  Marius Wischerhoff, Gerlind Plonka

Reconstruction of polygonal shapes from sparse Fourier samples.
Journal of Computational and Applied Mathematics 297 (2016), 117-131.
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[67]  Gerlind Plonka, Katrin Wannenwetsch

A deterministic sparse FFT algorithm for vectors with small support.
Numerical Algorithms, 71(4) (2016), 889-905.
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[66]  Gerlind Plonka, Yi Zheng

Relation between total variation and persistence distance and its application in signal processing.
Advances in Computational Mathematics 42(3) (2016), 651-674.
Download PDF (preprint, 2014)

[65]  Robert Beinert, Gerlind Plonka

Ambiguities in one-dimensional discrete phase retrieval from Fourier magnitudes.
Journal of Fourier Analysis and Applications 21(6) (2015), 1169-1198.
Download PDF (preprint, 2014)

[64]  Sebastian Hoffmann, G. Plonka, Joachim Weickert

Discrete Green's functions for harmonic and biharmonic inpainting with sparse atoms.
In X.-C. Tai et al. (Eds.): Energy Minimization Methods in Computer Vision and Pattern Recognition. LNCS 8932, Springer, Berlin, 2015, pp. 169-182.
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[63]  Mijail Guillemard, Dennis Heinen, Armin Iske, Sara Krause-Solberg, Gerlind Plonka

Adaptive Approximation Algorithms for Sparse Data Representation.
In S. Dahlke et al. (Eds.): Extraction of Quantifiable Information from Complex Systems. Lecture Notes in Computational Sciences and Engineering 102, 2014, pp. 281-302.
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[62]  Gerlind Plonka, Manfred Tasche

Prony methods for recovery of structured functions.
GAMM-Mitt. 37(2) (2014) 239-258.
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[61]  Stefan Loock, Gerlind Plonka

Phase retrieval for Fresnel measurements using a shearlet sparsity constraint.
Inverse Problems 30(5) (2014) 055005.
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[60] Gerlind Plonka, Armin Iske, Stefanie Tenorth.

Optimal representation of piecewise Hölder smooth bivariate functions by the easy path wavelet transform.
Journal of Approximation Theory 176 (2013), 42-67.
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[59]  Thomas Peter, Gerlind Plonka

A generalized Prony method for reconstruction of sparse sums of eigenfunctions of linear operators.
Inverse Problems 29 (2013), 025001.
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[58]  Gerlind Plonka, Marius Wischerhoff

How many Fourier samples are needed for real function reconstruction?
Journal of Applied Mathematics and Computing 42 (2013), 117-137.
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[57]  Thomas Peter, Gerlind Plonka, Daniela Rosca

Representation of sparse Legendre expansions.
Journal of Symbolic Computation 50 (2013), 159-169.
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[56] Daniela Rosca, Gerlind Plonka.

An area preserving projection from the regular octahedron to the sphere.
Results in Mathematics 62(3) (2012), 429-444, open access.
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[55]  Dennis Heinen, Gerlind Plonka

Wavelet shrinkage on paths for denoising of scattered data.
Results in Mathematics 62(3) (2012), 337-354, open access.
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[54]  Jianwei Ma, Gerlind Plonka, M. Yousuff Hussaini

Compressive Video Sampling with Approximate Message Passing Decoding.
IEEE Transactions on Circuits and Systems for Video Technology, 22(9) (2012), 1354-1364.
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[53]  Florian Boßmann, Gerlind Plonka, Thomas Peter, Oliver Nemitz, Till Schmitte

Sparse deconvolution methods for ultrasonic NDT.
Journal of Nondestructive Evaluation 31(3) (2012), 225-244, open access.
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[52] Gerlind Plonka, Stefanie Tenorth, Armin Iske.

Optimally sparse image representation by the easy path wavelet transform.
International Journal of Wavelets, Multiresolution and Information Processing 10(1) (2012),
1250007 (20 pages).
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[51] Daniela Rosca, Gerlind Plonka.

Uniform spherical grids via equal area projection from the cube to the sphere.
Journal of Computational and Applied Mathematics 236 (2011), 1033-1041.
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[50] Gerlind Plonka, Jianwei Ma.

Curvelet-wavelet regularized split Bregman iteration for compressed sensing.
International Journal of Wavelets, Multiresolution and Information Processing 9(1) (2011), 79-110.
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[49] Gerlind Plonka, Stefanie Tenorth, Daniela Rosca.

A hybrid method for image approximation using the easy path wavelet transform.
IEEE Transactions on Image Processing 20(2) (2011), 372-381.
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[48]  Jianwei Ma, Gerlind Plonka, Hervé Chauris.

A new sparse representation of seismic data using adaptive easy-path wavelet transform.
IEEE Geoscience and Remote Sensing Letters 7(3) (2010), 540-544.
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[47] Gerlind Plonka, Daniela Rosca.

Easy Path Wavelet Transform on triangulations of the sphere.
Mathematical Geosciences 42(7) (2010), 839-855.
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[46] Jianwei Ma, Gerlind Plonka.

The curvelet transform: A review of recent applications.
IEEE Signal Processing Magazine 27(2) (March 2010), 118-133.
Download PDF (Preprint, 32p.)
Download PDF (preprint, revised, 30p.)

[45]  Jens Krommweh, Gerlind Plonka.

Directional Haar wavelet frames on triangles.
Applied and Computational Harmonic Analysis 27 (2009), 215-234.
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[44] Gerlind Plonka.

The easy path wavelet transform: A new adaptive wavelet transform for sparse representation of two-dimensional data.
Multiscale Modeling and Simulation 7(3) (2009), 1474-1496.
Download PDF (preprint, revised version)

[43] Gerlind Plonka.

A digital diffusion-reaction type filter for nonlinear denoising.
Results in Mathematics, 53(3-4) (2009), 371-381.
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[42]  Gerlind Plonka, Daniela Rosca.

Sparse data representation on the sphere using the easy path wavelet transform.
In: Sampling Theory and Applications (SampTA'09), L. Fesquet and B. Torresani (eds.), 2009, 255–258, open access: http://hal.archives-ouvertes.fr/hal-00495456/en/.
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[41]  Gerlind Plonka, Stefanie Tenorth.

Nonlinear locally adaptive wavelet filter banks.
In: Sampling Theory and Applications (SampTA'09), L. Fesquet and B. Torresani (eds.), 2009, 381–384, open access: http://hal.archives-ouvertes.fr/hal-00495456/en/.
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[40] Jianwei Ma, Gerlind Plonka.

Computing with Curvelets: From Image Processing to Turbulent Flows.
Computing in Science and Engineering 11(2) (2009), 72-80.
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[39] Gerlind Plonka, Jianwei Ma.

Nonlinear regularized reaction-diffusion filters for denoising of images with textures.
IEEE Transactions on Image Processing 17(8) (2008), 1283-1294.
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[38] Gerlind Plonka, Hagen Schumacher, Manfred Tasche.

Numerical stability of biorthogonal wavelet transforms.
Advances in Computational Mathematics 29 (2008), 1-25.
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[37]  Jianwei Ma, Gerlind Plonka.

Combined curvelet shrinkage and nonlinear anisotropic diffusion.
IEEE Transactions on Image Processing 16 (2007), 2198-2206.
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[36] Gerlind Plonka, Jianwei Ma.

Convergence of an iterative nonlinear scheme for denoising of piecewise constant images.
International Journal of Wavelets, Multiresolution and Information Processing 5 (2007), 975-995.
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[35] Gerlind Plonka, Gabriele Steidl.

A multiscale wavelet-inspired scheme for nonlinear diffusion.
International Journal of Wavelets, Multiresolution and Information Processing 4 (2006), 1-22.
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[34] Gerlind Plonka, Manfred Tasche.

Fast and numerically stable algorithms for discrete cosine transforms.
Linear Algebra and its Applications 394 (2005), 309-345.
Download PDF (Preprint) Download PDF (technical report 2002)

[33] Gerlind Plonka, Manfred Tasche.

Numerical stability of fast trigonometric and orthogonal wavelet transforms.
Advances in Constructive Approximation: Vanderbilt (M. Neamtu, E.B. Saff, eds.), Nashboro Press, Brentwood, 2004, pp. 393-419.
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[32] Gerlind Plonka.

A global method for invertible integer DCT and integer wavelet algorithms.
Applied and Computational Harmonic Analysis 16 (2004), 90-110.
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[31] Gerlind Plonka, Ding-Xuan Zhou.

Properties of locally linearly independent function vectors.
Journal of Approximation Theory 122 (2003), 24-41.
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[30] Gerlind Plonka, Manfred Tasche.

Integer DCT-II by lifting steps.
International Series of Numerical Mathematics (W. Haussmann, K. Jetter, M. Reimer, J. Stöckler (eds.)), Vol.145, Birkhäuser, Basel, 2003, 235-252.
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[29] Gerlind Plonka, Manfred Tasche.

Invertible integer DCT algorithms.
Applied and Computational Harmonic Analysis 15 (2003), 70-88.
Download PDF (Preprint) Download PDF (technical report 2002)

[28] Gerlind Plonka.

How many holes can locally linearly independent refinable function vectors have?
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.
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[27] Di-Rong Chen, Gerlind Plonka.

Convergence of cascade algorithms in Sobolev spaces for perturbed refinement masks.
Journal of Approximation Theory 119 (2002), 133-155.
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[26] Kurt Jetter, Gerlind Plonka.

A survey on L2-Approximation order from shift-invariant spaces.
Multivariate Approximation and Applications (N. Dyn, D. Leviatan, D. Levin, A. Pinkus, eds.), Cambridge University Press, 2001, 73-111.
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[25] Gerlind Plonka, Amos Ron.

A new factorization technique for the matrix mask of univariate refinable functions.
Numerische Mathematik 87 (2001), 555-595.
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[24] Lothar Berg, Gerlind Plonka.

Some notes on two-scale difference equations.
Functional Equations and Inequalities (T.M. Rassias, ed.), Kluwer Academic Publishers, 2000, S. 7-29.
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[23] Lothar Berg, Gerlind Plonka.

Spectral properties of two-slanted matrices.
Results in Mathematics 35 (1999), 201-215
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[22] Lothar Berg, Gerlind Plonka.

Compactly supported solutions of two-scale difference equations.
Linear Algebra and its Applications 275 (1998), 49-75.
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[21] Gerlind Plonka, Vasily Strela.

Construction of multi-scaling functions with approximation and symmetry.
SIAM Journal on Mathematical Analysis 29 (1998), 481-510.
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[20] Gerlind Plonka, Vasily Strela.

From wavelets to multiwavelets.
Mathematical Methods of Curves and Surfaces II (M. Daehlen, T. Lyche, and L.L. Schumaker, eds.), Vanderbilt University Press, Nashville, 1998, 1-25.
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[19] Lothar Berg, Gerlind Plonka.

Refinement of vectors of Bernstein polynomials.
Rostocker Mathematisches Kolloquium 50 (1997), 19-30.
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[18] Gerlind Plonka.

Necessary and sufficient conditions for orthonormality of scaling vectors.
Multivariate Approximation and Splines (G. Nürnberger, J.W. Schmidt, G. Walz, eds.), ISNM Vol. 125, Birkhäuser, Basel, 1997, 205-218.
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[17] Gerlind Plonka.

On stability of scaling vectors.
Surface Fitting and Multiresolution Methods (A. Le Mehauté, C. Rabut, L. L. Schumaker, eds.), Vanderbilt University Press, Nashville, 1997, 293-300.
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[16] Albert Cohen, Ingrid Daubechies, Gerlind Plonka.

Regularity of refinable function vectors.
Journal of Fourier Analysis and Applications 3 (1997), 295-324.
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[15] Gerlind Plonka.

Approximation order provided by refinable function vectors.
Constructive Approximation 13 (1997), 221-244.
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[14] Gerlind Plonka.

Generalized spline wavelets.
Constructive Approximation 12 (1996), 127-155.
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[13] Gerlind Plonka.

Approximation properties of multi-scaling functions: A Fourier approach.
Rostocker Mathematisches Kolloquium 49 (1995), 115-126.
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[12] Gerlind Plonka.

Factorization of refinement masks of function vectors.
Wavelets and Multilevel Approximation (C. K. Chui, L. L. Schumaker, eds.), Singapore: World Scientific Publishing Co. 1995, 317-324.
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[11] Gerlind Plonka, Kathi Selig, Manfred Tasche.

On the construction of wavelets on a bounded interval.
Advances in Computational Mathematics 4 (1995), 357-388.
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[10] Gerlind Plonka.

Two-scale symbol and autocorrelation symbol for B-splines with multiple knots.
Advances in Computational Mathematics 3 (1995), 1-22.
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 [9] Gerlind Plonka, Manfred Tasche.

On the computation of periodic spline wavelets.
Applied and Computational Harmonic Analysis 2 (1995), 1-14.

 [8] Gerlind Plonka, Manfred Tasche.

A unified approach to periodic wavelets.
C. K. Chui, L. Montefusco & L. Puccio (Eds.). Wavelets: Theory, Algorithms, and Applications. Boston: Academic Press 1994, 137-151.
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 [7] Gerlind Plonka.

Spline wavelets with higher defect.
P. J. Laurent, A. Le Mehauté & L. L. Schumaker (Eds.). Wavelets, Images, and Surface Fitting. Boston: AKPeters 1994, 387-398.
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 [6] Gerlind Plonka, Manfred Tasche.

Cardinal Hermite spline interpolation with shifted nodes.
Mathematics of Computation 63 (1994), 645-659.

 [5] Gerlind Plonka.

Optimal shift parameters for periodic spline interpolation.
Numerical Algorithms 6 (1994), 297-316.
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 [4] Gerlind Plonka.

Periodic spline interpolation with shifted nodes.
Journal of Approximation Theory 76 (1994), 1-20.
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 [3] Gerlind Plonka.

An efficient algorithm for periodic Hermite spline interpolation with shifted nodes.
Numerical Algorithms 5 (1993), 51-62.

 [2] Gerlind Plonka.

Nonperiodic Hermite spline interpolation.
Rostocker Mathematisches Kolloquium 46 (1993), 65-74.

 [1] Gerlind Plonka, Manfred Tasche.

Efficient algorithms for the periodic Hermite spline interpolation.
Mathematics of Computation 58 (1992), 693-703.