Pierre Vandergheynst

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Approximating a signal or an image with a sparse linear expansion from an overcomplete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is ...

Wireless Body Sensor Nodes (WBSNs) are miniaturized and ultra-low-power devices, able to acquire and wirelessly trans- mit biosignals such as electrocardiograms (ECG) for extended periods of times and with little discomfort for subjects [1]. Energy efficiency is of paramount importance for WBSNs, because it allows a higher wearability (by requiring a smaller battery) and/or an increased mean time between charges. In this paper, we investigate how noise-aware design choices can be made to minimize energy con

The dynamics of neuron populations commonly evolve on low-dimensional manifolds. Thus, we need methods that learn the dynamical processes over neural manifolds to infer interpretable and consistent latent representations. We introduce a representation lear ...

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the ...

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the c ...

The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that the Fourier transform is. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many ...

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

Clustering on graphs has been studied extensively for years due to its numerous applications. However, in contrast to the classic problems, clustering in mobile and online social networks brings new challenges. In these scenarios, it is common that observational data contains multiple modalities of information reflecting different aspects of human behavior and social interactions. These interactions may be represented by a multi-layer graph that share the same set of vertices representing users, while havin

This paper introduces an algorithm for sparse approximation in redundant dictionaries, called the M-Term Pursuit (MTP), based on the matching pursuit approach (MP). This algorithm decomposes the signal into a linear combination of selected atoms, chosen to represent the signal components. The MTP algorithm provides adaptive representation for signals in any dictionary. The basic idea behind the MTP, is to partition the dictionary into

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disjoint sub-dictionaries, each carrying some meaningful information.

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is generic enough to find a lot of applications, for instance in multichannel signal compressed sensing (e.g. sensor networks, hyperspectral imaging) and compressive sparse principal component analysis (s-PCA). We assume data matrices have a simultaneous low-rank and joint sp

In this paper, we address the issues of analyzing and classifying JPEG 2000 code-streams. An original representation, called integral volume, is first proposed to compute local image features progressively from the compressed code-stream, on any spatial im ...

In many applications, the amount and resolution of digital images have significantly increased over the past few years. For this reason, there is a growing interest for techniques allowing to efficiently browse and seek information inside such huge data sp ...

This paper presents a novel method to correlate audio and visual data generated by the same physical phenomenon, based on sparse geometric representation of video sequences. The video signal is modeled as a sum of geometric primitives evolving through time, that jointly describe the geometric and motion content of the scene. The displacement through time of relevant visual features, like the mouth of a speaker, can thus be compared with the evolution of an audio feature to assess the correspondence between

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to algorithms for reconstructing missing information from graph signals via sparse representations, and yield new graph analysis tools. While previous work has focused on generalizing notions of

We propose a novel method for constructing wavelet transforms of functions defined on the vertices of an arbitrary finite weighted graph. Our approach is based on defining scaling using the the graph analogue of the Fourier domain, namely the spectral deco ...

Magnetic resonance imaging (MRI) probes signals through Fourier measurements. Accelerating the acquisition process is of major interest for various MRI applications. The recent theory of compressed sensing shows that sparse or compressible signals may be r ...

In this work, we explore a framework for the sparse representation of video sequences by means of spatio-temporal functions able to exploit the 2D nature of images as well as the temporal smoothness often associated to object trajectories. Decomposition over redundant dictionaries formed by 2D functions capable to exploit image geometry, or more precisely contours orientation, has shown to be well adapted for efficient sparse image approximations. Video representation by means of temporally evolving sets of

Approximating a signal or an image with a sparse linear expansion from an over-complete dictionary of atoms is an extremely useful tool to solve many signal processing problems. Finding the sparsest approximation of a signal from an arbitrary dictionary is ...

Proteins are typically represented by discrete atomic coordinates providing an accessible framework to describe different conformations. However, in some fields proteins are more accurately represented as near-continuous surfaces, as these are imprinted wi ...

New breakthroughs in image coding possibly rely in signal decomposition through non-separable basis functions. The work proposed in this paper provides an adaptive way of representing images as a sum of two-dimensional features. It presents a low bit-rate image coding method based on a Matching Pursuit expansion, over a dictionary built on anisotropic refinement and rotation of contour-like atoms. This method is shown to provide, at low bit-rates, results comparable to the state of the art in image compress

Pierre Vandergheynst

Chattez avec Graph Search

A simple test to check the optimality of a sparse signal approximation

Hardware-Software Inexactness in Noise-aware Design of Low-Power Body Sensor Nodes

MARBLE: interpretable representations of neural population dynamics using geometric deep learning

Vertex-Frequency Analysis on Graphs

Fast Robust PCA on Graphs

Fourier could be a data scientist: From graph Fourier transform to signal processing on graphs

Robust image reconstruction from multi-view measurements

Methods for Clustering Multi-Layer Graphs in Mobile Networks

Sparse Approximation Using M-Term Pursuits with Applications to Image and Video Compression

Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices

Scalable Feature Extraction for Coarse-to-Fine JPEG2000 Image Classification

Coarse-to-fine textures retrieval in the JPEG 2000 compressed domain for fast browsing of large image databases

Analysis of Multimodal Sequences Using Geometric Video Representations

Global and Local Uncertainty Principles for Signals on Graphs

Wavelets on graphs via spectral graph theory

Spread spectrum for compressed sensing techniques in magnetic resonance imaging

Video Representation Using Greedy Approximations Over Redundant Parametric Dictionaries

A simple test to check the optimality of sparse signal approximations

RosettaSurf-A surface-centric computational design approach

Low rate and scalable image coding with redundant representations