Prof. Dr. Gerlind Plonka

University of Duisburg-Essen, Faculty of Mathematics, Campus Duisburg

March 26, 2010

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

A hybrid method for image approximation using the easy path wavelet transform.
Universität Duisburg-Essen, Fakultät für Mathematik, Preprint, 2009, 19 p.
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[51] Gerlind Plonka, Stefanie Tenorth, Armin Iske.

Optimally sparse image representation by the easy path wavelet transform.
Universität Duisburg-Essen, Fakultät für Mathematik, Preprint, 2009, 16 p.
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[50]  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, 2010, to appear.
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[49] Gerlind Plonka, Jianwei Ma.

Curvelet-wavelet regularized split Bregman iteration for compressed sensing.
International Journal of Wavelets, Multiresolution and Information Processing, 2010, to appear.
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[48] Gerlind Plonka, Daniela Rosca.

Easy Path Wavelet Transform on triangulations of the sphere.
Mathematical Geosciences, 2010, to appear.
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[47] Jianwei Ma, Gerlind Plonka.

The curvelet transform: A review of recent applications.
IEEE Signal Processing Magazine 27(2) (March 2010), 118-133.
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[46]  Gerlind Plonka, Daniela Rosca.

Sparse data representation on the sphere using the easy path wavelet transform.
SAMPTA'09 - 8th International Conference on Sampling Theory and Applications, published online SampTa 2009.
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[45]  Gerlind Plonka, Stefanie Tenorth.

Nonlinear locally adaptive wavelet filter banks.
SAMPTA'09 - 8th International Conference on Sampling Theory and Applications, published online SampTa 2009.
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[44]  Jens Krommweh, Gerlind Plonka.

Directional Haar wavelet frames on triangles.
Applied and Computational Harmonic Analysis 27 (2009), 215-234.
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[43] 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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[42] Gerlind Plonka.

A digital diffusion-reaction type filter for nonlinear denoising.
Results in Mathematics, 53(3-4) (2009), 371-381.
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[41] 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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[40] 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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[39] Gerlind Plonka, Hagen Schumacher, Manfred Tasche.

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

Combined curvelet shrinkage and nonlinear anisotropic diffusion.
IEEE Transactions on Image Processing 16 (2007), 2198-2206.
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[37] 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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[36] 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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[35] Gerlind Plonka, Manfred Tasche.

Fast and numerically stable algorithms for discrete cosine transforms.
Linear Algebra and its Applications 394 (2005), 309-345.
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[34] 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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[33] 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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[32] Gerlind Plonka, Ding-Xuan Zhou.

Properties of locally linearly independent function vectors.
Journal of Approximation Theory 122 (2003), 24-41.
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[31] 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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[30] Gerlind Plonka, Manfred Tasche.

Invertible integer DCT algorithms.
Applied and Computational Harmonic Analysis 15 (2003), 70-88.
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[29] 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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[28] 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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[27] 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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[26] 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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[25] 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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[24] Lothar Berg, Gerlind Plonka.

Spectral properties of two-slanted matrices.
Results in Mathematics 35 (1999), 201-215
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[23] 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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[22] 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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[21] 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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[20] Lothar Berg, Gerlind Plonka.

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

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

[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.

 [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.

 [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.

 [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.

 [4] Gerlind Plonka.

Periodic spline interpolation with shifted nodes.
Journal of Approximation Theory 76 (1994), 1-20.

 [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.