University of Göttingen - Institute for Numerical and Applied Mathematics
Research group for Mathematical Signal and Image Processing
Publications


Preprints:
Graph regularized seismic dictionary learning
Lina Liu, Jianwei Ma, Gerlind Plonka
University of Göttingen, Institute for Numerical and Applied Mathematics, 2017, preprint as download.
A Deterministic Sparse FFT for Functions with Structured Fourier Sparsity
Sina Bittens, Ruochuan Zhang, Mark Iwen
University of Göttingen, Institute for Numerical and Applied Mathematics, and Michigan State University, Department of Mathematics, and Department of CMSE, March 2017, preprint as download.
Application of the AAK theory for sparse approximation of exponential sums
Gerlind Plonka, Vlada Pototskaia
University of Göttingen, Institute for Numerical and Applied Mathematics, 2016, preprint as download.
PARSE - A Pursuit Algorithm for Reconstruction of Spatial Events
Florian Boßmann
University of Göttingen, Institute for Numerical and Applied Mathematics, 2016, submitted.

2017:
Deterministic sparse FFT for M-sparse vectors
Gerlind Plonka, Katrin Wannenwetsch, Annie Cuyt, Wen-Shin Lee
Numerical Algorithms, to appear, 2017, revised preprint as download.
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
Robert Beinert, Gerlind Plonka
Applied and Computational Harmonic Analysis, to appear, 2017, preprint as download (arXiv).
Seismic data interpolation and denoising by learning a tensor tight frame
Lina Liu, Gerlind Plonka, Jianwei Ma
Inverse Problems, to appear, 2017, preprint as download.
A region based easy path wavelet transform for sparse image representation
Renato Budinich
International Journal of Wavelets, Multiresolution and Information Processing, to appear, 2017, preprint as download.
One-dimensional phase retrieval with additional interference measurements
Robert Beinert
Results Math., to appear, 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.
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.
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.
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:
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.
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:
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.



Research Group for Mathematical Signal and Image Processing

Institute for Numerical and Applied Mathematics
Lotzestr. 16-18
37083 Göttingen