Prof. Dr. Gerlind Plonka

University of Göttingen, Institute for Numerical and Applied Mathematics

January 16, 2020

Preprints:

[6]  Marzieh Hasannasab, Johannes Hertrich, Sebastian Neumayer, Gerlind Plonka, Simon Setzer, Gabriele Steidl

Parseval proximal neural networks.
Universität Göttingen, Institut für Numerische und Angewandte Mathematik, 2019.
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[5]  Ingeborg Keller and Gerlind Plonka

Modifications of Prony's method for the recovery and sparse approximation of generalized exponential sums.
Universität Göttingen, Institut für Numerische und Angewandte Mathematik, 2020.
Download PDF (arXiv preprint#2001.03651)

[4]  Marzieh Hasannasab, Sebastian Neumayer Gerlind Plonka, Simon Setzer, Gabriele Steidl and Jakob Geppert

Frame soft shrinkage as proximity operator.
Preprint 2019, (arXiv preprint#1910.02843)

[3]  Jakob Alexander Geppert and Gerlind Plonka

Frame soft shrinkage operators are proximity operators.
Universität Göttingen, Institut für Numerische und Angewandte Mathematik, 2019.
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[2]  Renato Budinich and Gerlind Plonka

A tree-based dictionary learning framework.
Universität Göttingen, Institut für Numerische und Angewandte Mathematik, 2019.
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[1]  Robert Beinert and Gerlind Plonka

One-Dimensional Discrete-Time Phase Retrieval.
Universität Göttingen, Institut für Numerische und Angewandte Mathematik, book chapter, 2018.
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Book:

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

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

Peer-reviewed publications:

[82]  Kilian Stampfer and Gerlind Plonka

The generalized operator-based Prony method.
Constructive Approximation, 2020, online first.
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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 (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.
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[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.

Non-peer-reviewed publications (proceedings)

[13]  Vlada Pototskaia, Gerlind Plonka

Application of the AAK theory and Prony-like Methods for sparse approximation of exponential sums.
Proc. Appl. Math. Mech. Volume 17, pp. 829-830, December 2017 (DOI 10.1002/pamm.201710385)

[12]  Robert Beinert, Gerlind Plonka

Sparse phase retrieval of structured signals by Prony's method.
Proc. Appl. Math. Mech. Volume 17, pp. 835-836, December 2017 (DOI 10.1002/pamm.201710382)

[11]  Stefan Loock, Gerlind Plonka

Iterative phase retrieval with sparsity constraints.
Proc. Appl. Math. Mech. Volume 16, Issue 1, pp. 835-836, October 2016 (DOI: 10.1002/pamm.201610406)

[10]  Gerlind Plonka, Vlada Pototskaia

Sparse approximation by Prony's method and AAK theory.
Oberwolfach Reports, 33/2016, 16-19.

[9]  Gerlind Plonka, Katrin Wannenwetsch

Deterministic sparse FFT algorithms.
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 667-668, October 2015 (DOI: 10.1002/pamm.201510323)

[8]  Thomas Peter, Gerlind Plonka, Robert Schaback

Prony's Method for Multivariate Signals.
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 665-666, October 2015 (DOI: 10.1002/pamm.201510322)

[7]  Robert Beinert, Gerlind Plonka

Ambiguities in one-dimensional phase retrieval of structured functions.
Proc. Appl. Math. Mech. Volume 15, Issue 1, pp. 653-654, October 2015 (DOI: 10.1002/pamm.201510316)

[6]  Gerlind Plonka, Katrin Wannenwetsch

A deterministic sparse FFT algorithm for vectors with short support.
Oberwolfach Reports, Volume 38/2015, pp. 41-44.

[5]  Thomas Peter, Gerlind Plonka

A generalized Prony method for sparse approximation.
Oberwolfach Reports 11/2013, pp. 600-602.

[4]  Thomas Peter, Gerlind Plonka

Approximation by k-sparse sums of eigenfunctions of linear operators.
Oberwolfach Reports 31/2012, pp.16-18.

[3]  Gerlind Plonka, Jianwei Ma

Curvelets.
in Encyclopedia of Applied and Computational Mathematics, B. Engquist (eds.), Springer Berlin, 2015, DOI 10.1007/978-3-540-70529-1.

[2]  Gerlind Plonka, Stefanie Tenorth, Daniela Rosca.

Image approximation by a hybrid method based on the easy path wavelet transform.
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers, 2009, 442-446. ISBN: 978-1-4244-5825-7.

[1] Gerlind Plonka.

Stability of translates of scaling vectors.
Computational Mathematics (Achim Sydow, ed.), Wissenschaft & Technik Verlag, Berlin, 1997, 81-86.