Pierre Vandergheynst

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Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To attain scalability for large graphs, fast graph-signal filtering techniques are needed. In this contribution, we propose an accelerated algorithm based on the Lanczos method that adapts to the Laplacian spectrum without explicitly computing it. The result is an accurate,

To be efficient, data protection algorithms should generally exploit the properties of the media information in the transform domain. In this paper, we will advocate the use of non-linear image approximations using highly redundant dictionaries, for security algorithms. We show that a flexible image representation based on a multidimensional and geometry-based coding scheme, has precious attributes for security information embedding. Redundant expansions provide very good approximation properties, as well a

We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s2MRI, consists of pre-modulating the signal of interest by a linear chirp before rando ...

In this report we study the problem of sparse signal approximation over redundant dictionaries. We focus our attention on the minimization of a cost function where the error is measured using a l1 norm. We show a constructive equivalence between this minimization and Linear Programming. A recovery condition is then proved and finally we provide an example of the use of such a technique for denoising.

Mining useful clusters from high dimensional data has received sig- nificant attention of the signal processing and machine learning com- munity in the recent years. Linear and non-linear dimensionality reduction has played an important role to overcome the curse of di- mensionality. However, often such methods are accompanied with problems such as high computational complexity (usually associated with the nuclear norm minimization), non-convexity (for matrix fac- torization methods) or susceptibility to gr

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode ...

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) × R*+, embedded into the Lorentz group SOo(3,1) via the Iwasawa decomposition, and X -SOo(3,1)/. The space L2(S2,d) carries a unitary irreducible representation of SOo(3,1), which is square integrable over X, and thus yields the wavelets on S2 and the associate

In this work, we propose a new, fast and scalable method for anomaly detection in large time-evolving graphs. It may be a static graph with dynamic node attributes (e.g. time-series), or a graph evolving in time, such as a temporal network. We define an an ...

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 ...

In this work we explore the potentialities of a framework for the representation of audio-visual signals using decompositions on overcomplete dictionaries. Redundant decompositions may describe audio-visual sequences in a concise fashion, preserving good representation properties thanks to the use of redundant, well designed, dictionaries. We expect that this will help us overcome two typical problems of multimodal fusion algorithms. On one hand, classical representation techniques, like pixel-based measure

This paper investigates intra-adaptive wavelets for video coding with frame-adaptive motion-compensated lifted wavelet transforms. With motion-compensated lifted wavelets, the temporal wavelet decomposition operates along motion trajectories. However, valid trajectories for efficient multi-scale filtering have a finite duration in time. This is due to well known effects like occlusions or inaccurate motion estimation. These discontinuities may generate many non-zero wavelet coefficients when a transform wit

In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, namely the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invaria ...

This paper proposes a multiresolution Matching Pursuit decomposition of natural images. Matching Pursuit is a greedy algorithm that decomposes any signal into a linear expansion of waveforms taken from a redundant dictionary, by iteratively picking the waveform that best matches the input signal. Since the computational cost rapidly grows with the size of the signal, we propose a multiresolution strategy that, together with a dictionary training, significantly reduces the encoding complexity while still pro

This paper proposes a multiresolution Matching Pursuit decomposition of natural images. Matching Pursuit is a greedy algorithm that decomposes any signal into a linear expansion of waveforms taken from a redundant dictionary, by iteratively picking the waveform that best matches the input signal. Since the computational cost rapidly grows with the size of the signal, we propose a multiresolution strategy that, together with an efficient dictionary, significantly reduces the encoding complexity while still p

Relationships between entities in datasets are often of multiple types, which can naturally be modeled by a multi-layer graph; a common vertex set represents the entities and the edges on different layers capture different types of relationships between th ...

Detecting that pedestrians are present in front of a vehicle is highly desirable to avoid dangerous traffic situations. A novel vision-based system is presented to automatically detect far-away pedestrians with low-resolution cameras mounted in vehicles gi ...

This paper introduces a sparse signal representation algorithm in redundant dictionaries, called the M-Term Pursuit (MTP), with an application to image representation and scalable coding. The MTP algorithm belongs to the framework of the matching pursuit (MP); it expands the image into a linear combination of atoms, selected from a large collection of spatial atoms. The MTP relies on the concept of dictionary partitioning, i.e., as splitting the dictionary into

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disjoint sub-dictionaries, each carrying s

In this work, we present Multimodal Equivariant Inverse Design Network (MEIDNet), a framework that jointly learns structural information and materials properties through contrastive learning, while encoding structures via an equivariant graph neural network (EGNN). By combining generative inverse design with multimodal learning, our approach accelerates the exploration of chemical-structural space and facilitates the discovery of materials that satisfy predefined property targets. MEIDNet exhibits strong la

Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets. In this context, it is of high importance to develop flexible models of signals defined over graphs or networks. In this paper, we generalize the traditional concept of wide sense stationarity to signals defined over the vertices of arbitrary weighted undirected graphs. We show that stationarity is intimately linked to statistical invariance under a localization o

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution provides an optimize ...

Pierre Vandergheynst

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Accelerated filtering on graphs using Lanczos method

Redundant Image Representations in Security Applications

Spread spectrum magnetic resonance imaging

Sparse Approximation by Linear Programming: Measuring the Error with the $ell_1$ Norm

PCA using graph total variation

Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation

Wavelets on the 2-sphere and related manifolds

Anomaly detection in the dynamics of web and social networks

Low rate and flexible image coding with redundant representations

Analysis of Multimodal Signals Using Redundant Representations

Intra-Adaptive Motion-Compensated Lifted Wavelets for Video Coding

Matching pursuit-based shape representation and recognition using scale-space

Evolutionary Multiresolution Matching Pursuit and its relations with the Human Visual System

Evolutionary Multiresolution Matching Pursuit and its Relations with the Human Visual System

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

Robust Real-time Pedestrians Detection in Urban Environments with a Network of Low Resolution Cameras

The M-Term Pursuit for Image Representation and Progressive Compression

MEIDNet: Multimodal generative AI framework for inverse materials design

Stationary signal processing on graphs

On Variable Density Compressive Sampling