Pierre Vandergheynst

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The spectral graph wavelet transform (SGWT) defines wavelet transforms appropriate for data defined on the vertices of a weighted graph. Weighted graphs provide an extremely flexible way to model the data domain for a large number of important applications (such as data defined on vertices of social networks, transportation networks, brain connectivity networks, point clouds, or irregularly sampled grids). The SGWT is based on the spectral decomposition of the N×N graph Laplacian matrix L, where N is the nu

Acoustical behavior of a room for a given position of microphone and sound source is usually described using the room impulse response. If we rely on the standard uniform sampling, the estimation of room impulse response for arbitrary positions in the room ...

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This technical report is organized as follows: In the first section we develop the Laplacian operator on non-Euclidean manifolds. First we start by derivation of Laplacian operator on Riemannian manifolds and than we derive it explicitly for each of the non-Euclide

In this paper, we propose a variational model to segment an object belonging to a given scale space using the active contour method, a geometric shape prior and the Mumford-Shah functional. We define an energy functional composed by three complementary terms. The first one detects object boundaries from image gradients. The second term constrains the active contour to get a shape compatible with a statistical shape model of the shape of interest. And the third part drives globally the shape prior and the ac

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year WMAP data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifyin ...

This report presents a new method to confront the Blind Audio Source Separation (BASS) problem, by means of audio and visual information. In a given mixture, we are able to locate the video sources first and, posteriorly, recover each source signal, only with one microphone and the associated video. The proposed model is based on the Matching Pursuit (MP) [18] decomposition of both audio and video signals into meaningful structures. Frequency components are extracted from the soundtrack, with the consequent

Low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their ...

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the spectral decomposition of the discrete graph Laplacian

\L

. Given an arbitrary measurable function g, the spectral decomposition allows one to define the operator

T_g=g(\L)

. Scaling by

t

may then be defined by

T_g^t = g(t\L)

. Our graph wavelets $W_{t,

Relationships between entities in datasets are often of multiple nature, like geographical distance, social relationships, or common interests among people in a social network, for example. This information can naturally be modeled by a set of weighted and ...

Gaussian processes (GPs) are popular nonparametric statistical models for learning unknown functions and quantifying the spatiotemporal uncertainty in data. Recent works have extended GPs to model scalar and vector quantities distributed over non-Euclidean domains, including smooth manifolds appearing in numerous fields such as computer vision, dynamical systems, and neuroscience. However, these approaches assume that the manifold underlying the data is known, limiting their practical utility. We introduce

Atrial Fibrillation (AF) is the most common type of human arrhythmia. Beside its clinical description as absolute arrhythmia, its diagnosis has been assessed for years by visual inspection of the surface electrocardiogram (ECG). Due to the much higher amplitude of the electrical ventricular activity, the analysis of atrial fibrillation requires the previous isolation of the atrial activity component. In this work, an approach to separate atrial and ventricular signal components, decomposing the signal over

Machine learning for protein modeling faces significant challenges due to proteins' inherently dynamic nature, yet most graph-based machine learning methods rely solely on static structural information. Recently, the growing availability of molecular dynam ...

We propose a new framework for the analysis of low- rank tensors which lies at the intersection of spectral graph theory and signal processing. As a first step, we present a new graph based low-rank decomposition which approximates the classical low-rank S ...

High-dimensional data are often assumed to lie on lower-dimensional manifolds. We study how to construct diffusion processes on this data manifold using only point cloud samples and without access to charts, projections, or other geometric primitives. Here, we introduce Implicit Manifold-valued Diffusions (IMDs), a datadriven mathematical formalism for defining stochastic differential equations in the original high-dimensional space that describe drifting Brownian particles evolving intrinsically on the und

The study of brain dynamics enables us to characterize the time-varying functional connectivity among distinct neural groups. However, current methods suffer from the absence of structural connectivity information. We propose to integrate infra-slow neural ...

We propose a novel method to accurately reconstruct a set of images representing a single scene from a few linear multiview measurements. Each observed image is modeled as the sum of a background image and a foreground one. The background image is common t ...

In this paper, we describe a method to infer 3-D scene information using a single view captured by an omnidirectional camera. The proposed technique is inscribed in the so called ``Shape from Texture'' problem : if the textures hold by 3-D surfaces respect ...

Deep generative models often face a fundamental tradeoff: high sample quality can come at the cost of memorisation, where the model reproduces training data rather than generalising across the underlying data geometry. We introduce Carré du champ flow matching (CDC-FM), a generalisation of flow matching (FM), that improves the quality-generalisation tradeoff by regularising the probability path with a geometry-aware noise. Our method replaces the homogeneous, isotropic noise in FM with a spatially varying,

The specific issue addressed in this paper is tailoring specific functionality to allow a group of teachers and students to carry out the learning process in Digital Signal and Image Processing in an electronic virtual environment that is meant to replace the physical class environment. In order such an environment to be performed, not only the course content itself but also different Web-based tools for interaction between the students and teachers are needed. A Graphical User Interface (GUI), designed and

We study the problem of sampling

k

-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, \ie, independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than

O(\nbClass \log(\nbClass))

measurements are sufficient to ensure an accurate and stable recovery of

Pierre Vandergheynst

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The Spectral Graph Wavelet Transform: Fundamental Theory and Fast Computation

Joint Estimation Of The Room Geometry And Modes With Compressed Sensing

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

A Variational Model for Object Segmentation Using Boundary Information, Statistical Shape Prior and the Mumford-Shah Functional

Alignment and signed-intensity anomalies in WMAP data

Blind Audio-Visual Source Separation Using Sparse Redundant Representations

Image compression using an edge adapted redundant dictionary and wavelets

Wavelets on Graphs via Spectral Graph Theory

Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds

Implicit Gaussian Process Representation of Vector Fields Over Arbitrary Latent Mani-Folds

Sparse Decompositions for Ventricular and Atrial Activity Separation

Boosting Protein Graph Representations through Static-Dynamic Fusion

Multilinear Low-Rank Tensors on Graphs & Applications

Diffusion Processes on Implicit Manifolds

Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems

Robust Image Reconstruction from Multiview Measurements

Shape from Texture for Omnidirectional Images

Carré du champ flow matching: better quality-generalisation tradeoff in generative models

Virtual classroom for multimedia teaching on WWW

Random sampling of bandlimited signals on graphs