Discrete Laplace operator

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Restriction of 3D arithmetic Laplace eigenfunctions to a plane

Riccardo Walter Maffucci

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure ('length') of nodal intersections against a smooth 2-dimensional toral sub-manifold ('surface'). A prior result of ours pr ...

2020

Graph-based Transform Coding with Application to Image Compression

Pascal Frossard, Ntorina Thanou, Giulia Fracastoro

In this paper, we propose a new graph-based coding framework and illustrate its application to image compression. Our approach relies on the careful design of a graph that optimizes the overall rate-distortion performance through an effective graph-based t ...

2019

GOT: An Optimal Transport framework for Graph comparison

Pascal Frossard, Hermina Petric Maretic, Mireille El Gheche, Giovanni Chierchia

We present a novel framework based on optimal transport for the challenging problem of comparing graphs. Specifically, we exploit the probabilistic distribution of smooth graph signals defined with respect to the graph topology. This allows us to derive an ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

Optimized Quantization in Distributed Graph Signal Filtering

Pascal Frossard, Isabela Cunha Maia Nobre

Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to implement message ...

2019

Weyl-type bounds for Steklov eigenvalues

Joachim Stubbe, Luigi Provenzano

We present upper and lower bounds for Steklov eigenvalues for domains in RN+1 with C-2 boundary compatible with the Weyl asymptotics. In particular, we obtain sharp upper bounds on Riesz-means and the trace of corresponding Steklov heat kernel. The key res ...

EUROPEAN MATHEMATICAL SOC2019

Graph Spectral Analysis Of Voxel-Wise Brain Graphs From Diffusion-Weighted Mri

Dimitri Nestor Alice Van De Ville, Hamid Behjat, Anjali Bagunu Tarun

Non-invasive characterization of brain structure has been made possible by the introduction of magnetic resonance imaging (MRI). Graph modeling of structural connectivity has been useful, but is often limited to defining nodes as regions from a brain atlas ...

IEEE2019

A Preconditioned Graph Diffusion LMS for Adaptive Graph Signal Processing

Ali H. Sayed, Roula Nassif

Graph filters, defined as polynomial functions of a graph-shift operator (GSO), play a key role in signal processing over graphs. In this work, we are interested in the adaptive and distributed estimation of graph filter coefficients from streaming graph s ...

IEEE COMPUTER SOC2018

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

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associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Robust and Efficient Data Clustering with Signal Processing on Graphs

Lionel Jérémie Martin

Data is pervasive in today's world and has actually been for quite some time. With the increasing volume of data to process, there is a need for faster and at least as accurate techniques than what we already have. In particular, the last decade recorded t ...

EPFL2018

Spectrally approximating large graphs with smaller graphs

Pierre Vandergheynst, Andreas Loukas

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...

2018

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associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018