23 citations · 64 across the 21 of their papers we have counts for
28 papers
-adaptive trees for graph signal approximation
Giacomo Elefante, Wolfgang Erb, Michael Multerer
Tree-encoded partitionings of graphs are fundamental tools for the decomposition and approximation of graph signals. For the efficient approximation of such graph signals, we devel…
Highly Localized RBF Lagrange Functions for Finite Difference Methods on Spheres
Wolfgang Erb, Thomas Hangelbroek, Francis J. Narcowich +2
The aim of this paper is to show how rapidly decaying RBF Lagrange functions on the spheres can be used to create effective, stable finite difference methods based on radial basis…
Krylov subspace methods to accelerate kernel machines on graphs
Wolfgang Erb
In classical frameworks as the Euclidean space, positive definite kernels as well as their analytic properties are explicitly available and can be incorporated directly in kernel-b…
Interpolation with the polynomial kernels
Giacomo Elefante, Wolfgang Erb, Francesco Marchetti +3
The polynomial kernels are widely used in machine learning and they are one of the default choices to develop kernel-based classification and regression models. However, they are r…
Graph Wedgelets: Adaptive Data Compression on Graphs based on Binary Wedge Partitioning Trees and Geometric Wavelets
Wolfgang Erb
We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph par…
On Kosloff Tal-Ezer Least-Squares Quadrature Formulas
Giacomo Cappellazzo, Wolfgang Erb, Francesco Marchetti +1
In this work, we study a global quadrature scheme for analytic functions on compact intervals based on function values on quasi-uniform grids of quadrature nodes. In practice it is…
Simple Graph Convolutional Networks
Luca Pasa, Nicolò Navarin, Wolfgang Erb +1
Many neural networks for graphs are based on the graph convolution operator, proposed more than a decade ago. Since then, many alternative definitions have been proposed, that tend…
Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization
Salvatore Cuomo, Wolfgang Erb, Gabriele Santin
The inference of novel knowledge, the discovery of hidden patterns, and the uncovering of insights from large amounts of data from a multitude of sources make Data Science (DS) to…
Partition of Unity Methods for Signal Processing on Graphs
Roberto Cavoretto, Alessandra De Rossi, Wolfgang Erb
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation sc…
A new 3D model for magnetic particle imaging using realistic magnetic field topologies for algebraic reconstruction
Gaël Bringout, Wolfgang Erb, Jürgen Frikel
We derive a new 3D model for magnetic particle imaging (MPI) that is able to incorporate realistic magnetic fields in the reconstruction process. In real MPI scanners, the generate…
Semi-Supervised Learning on Graphs with Feature-Augmented Graph Basis Functions
Wolfgang Erb
For semi-supervised learning on graphs, we study how initial kernels in a supervised learning regime can be augmented with additional information from known priors or from unsuperv…
Graph signal interpolation with Positive Definite Graph Basis Functions
Wolfgang Erb
For the interpolation of graph signals with generalized shifts of a graph basis function (GBF), we introduce the concept of positive definite functions on graphs. This concept merg…
Anisotropic Gaussian approximation in
Wolfgang Erb, Thomas Hangelbroek, Amos Ron
Let be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in dimensions. is used pervasiv…
Shapes of Uncertainty in Spectral Graph Theory
Wolfgang Erb
We present a flexible framework for uncertainty principles in spectral graph theory. In this framework, general filter functions modeling the spatial and spectral localization of a…
Shape-Driven Interpolation with Discontinuous Kernels: Error Analysis, Edge Extraction and Applications in MPI
Stefano De Marchi, Wolfgang Erb, Francesco Marchetti +2
Accurate interpolation and approximation techniques for functions with discontinuities are key tools in many applications as, for instance, medical imaging. In this paper, we study…
Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk
Wolfgang Erb
Rhodonea curves are classical planar curves in the unit disk with the characteristic shape of a rose. In this work, we use point samples along such rose curves as node sets for a n…
Weak limits for weighted means of orthogonal polynomials
Wolfgang Erb
This article is a first attempt to obtain weak limit formulas for weighted means of orthogonal polynomials. For this, we introduce a new mean Nevai class that guarantees the existe…
A spectral interpolation scheme on the unit sphere based on the nodes of spherical Lissajous curves
Wolfgang Erb
For sampling values along spherical Lissajous curves we establish a spectral interpolation and quadrature scheme on the sphere. We provide a mathematical analysis of spherical Liss…
Mathematical Analysis of the 1D Model and Reconstruction Schemes for Magnetic Particle Imaging
Wolfgang Erb, Andreas Weinmann, Mandy Ahlborg +10
Magnetic particle imaging (MPI) is a promising new in-vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response i…
A unifying theory for multivariate polynomial interpolation on general Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb
The goal of this article is to provide a general multivariate framework that synthesizes well-known non-tensorial polnomial interpolation schemes on the Padua points, the Morrow-Pa…
Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb, Yurii Kolomoitsev +1
To analyze the absolute condition number of multivariate polynomial interpolation on Lissajous-Chebyshev node points, we derive upper and lower bounds for the respective Lebesgue c…
Multivariate polynomial interpolation on Lissajous-Chebyshev nodes
Peter Dencker, Wolfgang Erb
In this article, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets related to Lissajous curves and Chebyshev varieties. After clas…
Bivariate Lagrange interpolation at the node points of Lissajous curves - the degenerate case
Wolfgang Erb
In this article, we study bivariate polynomial interpolation on the node points of degenerate Lissajous figures. These node points form Chebyshev lattices of rank and are gener…
Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves
Wolfgang Erb, Christian Kaethner, Mandy Ahlborg +1
Motivated by an application in Magnetic Particle Imaging, we study bivariate Lagrange interpolation at the node points of Lissajous curves. The resulting theory is a generalization…