Preprints

  • Erb, W. Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets. arXiv:2110.08843 (2021) (Preprint) (Software)
  • Cappellazzo, G., Erb, W., Marchetti, F., and Poggiali, D. On Kosloff Tal-Ezer least-squares quadrature formulas. arXiv:2109.13138 (2021) (Preprint) (Code) (Poster)
  • Cuomo, S., Erb, W. and Santin, G. Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization. arXiv:2103.01575 (2021) (Preprint)
  • Erb, W. Semi-Supervised Learning on Graphs with Feature-Augmented Graph Basis Functions. arXiv:2003.07646 (2020) (Preprint) (Software GBFlearn)
  • Erb, W., Hangelbroek, T. and Ron, A. Anisotropic Gaussian approximation in $L_2(\mathbb{R}^2)$. arXiv:1910.10319 (2019) (Preprint)
  • Dencker, P. and Erb, W. A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes. arXiv:1711.00557 (2017) (Preprint) (Software 2D) (Software 3D) (Slides) (LC2Dfevalapp) (LC2Dplotapp)

2022

  • Erb, W. Graph Signal Interpolation with Positive Definite Graph Basis Functions. Appl. Comput. Harmon. Anal. 60 (2022), 368-395 (Preprint)

2021

  • Cavoretto, R., De Rossi, A., and Erb, W. Partition of Unity Methods for Signal Processing on Graphs. J. Fourier Anal. Appl. 27 (2021), Art. 66 (Preprint)
  • Erb, W. Shapes of Uncertainty in Spectral Graph Theory. IEEE Trans. Inform. Theory 67:2 (2021), 1291-1307 (Preprint) (Software GUPPY)
  • Erb, W. Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk. Constr. Approx. 53:2, 281-318 (2021) (Preprint) (Software RDisk) (Rhodonea curves) (Poster)

2020

  • Bringout, G., Erb, W. and Frikel, J. A new 3D model for Magnetic Particle Imaging using realistic magnetic field topologies for algebraic reconstruction. Inverse Problems 36 (2020), 124002 (Preprint)
  • Navarin, N., Erb, W., Pasa, L., and Sperduti, A. Linear Graph Convolutional Networks. ESANN 2020 - Proceedings, 28th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (2020), 151–156 (Publication)
  • De Marchi, S., Erb, W., Francomano, E., Marchetti, F., Perracchione, E. and Poggiali, D. Fake Nodes approximation for Magnetic Particle Imaging. MELECON 2020 - Proceedings, 20th IEEE Mediterranean Electrotechnical Conference (2020), 434-438, 9140583
  • De Marchi, S., Erb, W., Marchetti, F., Perracchione, E. and Rossini, M. Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in Magnetic Particle Imaging. SIAM J. Sci. Comput. 42:2 (2020), B472-B491 (Preprint) (Poster)
  • Erb, W. A spectral interpolation scheme on the unit sphere based on the nodes of spherical Lissajous curves. IMA J. Numer. Anal. 40:2 (2020), 1330–1355 (Preprint) (Software LSphere) (Spherical Lissajous curves)
  • Erb, W. Weak limits for weighted means of orthogonal polynomials. J. Spectral Theory 10:3 (2020), 787–808 (Preprint)

2018

  • Erb, W., Weinmann, A., Ahlborg, M., Brandt, C., Bringout, G. , Buzug, T.M, Frikel J., Kaethner, C., Knopp, T., März, T., Möddel, M., Storath, M. and Weber, A. Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging. Inverse Problems 34 (2018), 055012 (Preprint) (Slides)

2017

  • Dencker, P., Erb, W., Kolomoitsev, Y. and Lomako, T. Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes. Journal of Complexity 43, (2017), 1-27 (Preprint)
  • Dencker, P. and Erb, W. Multivariate polynomial interpolation on Lissajous-Chebyshev nodes. J. Approx. Theory 219 (2017), 15-45 (Preprint) (Software) (Slides)
  • Schmiester, L., Moddel, M., Erb, W. and Knopp, T. Direct Image Reconstruction of Lissajous Type Magnetic Particle Imaging Data using Chebyshev-based Matrix Compression. IEEE Transactions on Computational Imaging 3:4 (2017), 671-681
  • De Marchi, S., Erb, W. and Marchetti, F. Spectral filtering for the reduction of the Gibbs phenomenon for polynomial approximation methods on Lissajous curves with applications in MPI. Dolomites Res. Notes Approx. 10 (2017), 128-137 (Publication)
  • De Marchi, S., Erb, W. and Marchetti, F. Lissajous sampling and spectral filtering in MPI applications: the reconstruction algorithm for reducing the Gibbs phenomenon. SampTA 2017, 12th International Conference on Sampling Theory and Applications (2017), 580-584, 8024375

2016

  • Kaethner, C., Erb, W., Ahlborg, M., Szwargulski, P., Knopp, T. and Buzug, T. M. Non-Equispaced System Matrix Acquisition for Magnetic Particle Imaging based on Lissajous Node Points. IEEE Transactions on Medical Imaging 35:11 (2016), 2476-2485
  • Erb, W. Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case. Appl. Math. Comput. 289 (2016), 409-425 (Preprint)
  • Erb, W., Kaethner, C., Ahlborg, M. and Buzug, T.M. Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves. Numer. Math. 133:4 (2016), 685-705 (Preprint) (Software)

2015

  • Erb, W., Kaethner, C., Dencker, P., and Ahlborg, M. A survey on bivariate Lagrange interpolation on Lissajous nodes. Dolomites Research Notes on Approximation 8 (Special issue) (2015), 23-36 (Publication) (Software)
  • Erb, W. und Semenova, E.V. On adaptive discretization schemes for the solution of ill-posed problems with semiiterative methods. Appl. Anal. 94:10 (2015), 2057-2076 (Preprint)
  • Erb, W. und Mathias, S. An alternative to Slepian functions on the unit sphere - A space-frequency analysis based on localized spherical polynomials. Appl. Comput. Harmon. Anal. 38:2 (2015), 222-241 (Preprint)
  • Erb, W. Accelerated Landweber methods based on co-dilated orthogonal polynomials. Numer. Alg. 68:2 (2015), 229-260 (Preprint)

2013

  • Erb, W. An orthogonal polynomial analogue of the Landau-Pollak-Slepian time-frequency analysis. J. Approx. Theory 166 (2013), 56-77 (Preprint)

2012

  • Erb, W. Optimally space localized polynomials with applications in signal processing. J. Fourier Anal. Appl. 18:1 (2012), 45-66 (Preprint)

2011

  • Erb, W., and Toókos, F. Applications of the monotonicity of extremal zeros of orthogonal polynomials in interlacing and optimization problems. Appl. Math. Comput. 217:9 (2011), 4771-4780 (Preprint)

2010

  • Erb, W. Uncertainty principles on compact Riemannian manifolds. Appl. Comput. Harmon. Anal. 29:2 (2010), 182-197 (Preprint)
  • Erb, W. Uncertainty principles on Riemannian manifolds. TU München (2010), Dissertation

2008

  • Erb, W., and Filbir, F. Approximation by positive definite functions on compact groups. Numer. Funct. Anal. Optim. 29:9-10 (2008), 1082-1107 (Preprint)