Pierre Vandergheynst

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Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

Rare-event transitions in metastable systems are expensive to sample because direct simulation spends most of its time in long-lived basins, and only rarely undergo transitions. We study whether Implicit Manifold-valued Diffusions (IMDs), learned directly from trajectory point clouds, can act as data-driven surrogates of the transport geometry underlying such transitions. Our central hypothesis is that when the training cloud is drawn from a biased dynamical ensemble (such as successful reactive trajectorie

Building good sparse approximations of functions is one of the major themes in approximation theory. When applied to signals, images or any kind of data, it allows to deal with basic building blocks that essentially synthesize all the information at hand. It is known since the early successes of wavelet analysis that sparse expansions very often result in efficient algorithms for characterizing signals in noise or even for analyzing and compressing signals. The very strong links between approximation theory

The purpose of this paper is to extend results by Villemoes and Temlyakov about exponential convergence of Matching Pursuit with some structured dictionaries for ``simple'' functions in finite or infinite dimension. Our results are based on an extension of ...

Translation elongation plays a key role in cellular homeostasis, and dysregulation of this process has been implicated in various diseases and metabolic disorders. Uncovering the causes of intragenic heterogeneity of translation, especially in contexts of different amino acid deprivations, could help increase our understanding of these disorders and pave the way for novel therapeutics. Ribosome profiling provides accurate measurements for the genome-wide ribosome footprints, which could be utilized to inves

This paper presents a progressive coding scheme for 3D objects, based on an overcomplete decomposition of the 3D model on a sphere. Due to increased freedom in the bases construction, redundant expansions have shown interesting approximation properties in the decomposition of signals with multidimensional singularities organized along embedded submanifolds. We propose to map simple 3D models on 2D spheres and then to decompose the signal over a redundant dictionary of oriented and anisotropic atoms that liv

Most of the multi-camera systems assume a well structured environment to detect and match objects across cameras. Cameras need to be fixed and calibrated. In this work, a novel system is presented to detect and match any objects in a network of uncalibrate ...

To retrieve scene informations using a single omnidirectional camera, we have based our work on a shape from texture method proposed by Lindeberg. To do so, we have adapted the method of Lindeberg, that was developed for planar images, in order to use it on the sphere S2 . The mathematical tools we use are stereographic dilation to implement scale variations for the scale-space representation, and ﬁlter steerability on the sphere to decrease computational order. The texture distortions due to the pro jectio

In the present paper we propose a new framework for the construction of meaningful dictionaries for sparse representation of signals. The dictionary approach to coding and compression proves very attractive since decomposing a signal over a redundant set of basis functions allows a parsimonious representation of information. This interest is witnessed by numerous research efforts that have been done in the last years to develop efficient algorithm for the decomposition of signals over redundant sets of func

Estimation of the location of sound sources is usually done using microphone arrays. Such settings provide an environment where we know the difference between the received signals among different microphones in the terms of phase or attenuation, which enab ...

This paper provides new results on computing simultaneous sparse approximations of multichannel signals over redundant dictionaries using two greedy algorithms. The first one, p-thresholding, selects the S atoms that have the largest

p

-correlation while ...

We propose a universal and efficient compressive sampling strategy based on the use of a spread spectrum technique. The method essentially consists in a random pre-modulation of the signal of interest followed by projections onto randomly selected vectors ...

We address the problem of blind audio source separation in the under-determined and convolutive case. The contribution of each source to the mixture channels in the time-frequency domain is modeled by a zero-mean Gaussian random vector with a full rank cov ...

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first iss ...

Very 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 multiscale nature and in their ability to sparsely represent functions that are piecewise smooth. Their main problem on the other hand, is that in 2-D wavelets are not able to deal with the natural geometry of images, i.e they cannot sparsely represe

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary t ...

In this paper we consider recovery of a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model which can efficiently restricts the degrees of freedom of data and, at the same time, is generic so that finds varieties of applications, namely, in multichannel signal compressed sensing (e.g. sensor networks, hyperspectral imaging) and compressive sparse principal component analysis (s-PCA). We assume data matrices to have a simultaneous low-rank and joint s

In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by thre ...

We extend the domain of application of a method developed recently for joint reconstruction of l images, representing the same scene, from few multi-view measurements. While this method was initially designed for planar scenes, we show here that parametric ...

Translation elongation plays an important role in regulating protein concentrations in the cell, and dysregulation of this process has been linked to several human diseases. In this study, we use data from ribo-seq experiments to model ribosome densities, ...

Pierre Vandergheynst

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Geometric deep learning: going beyond Euclidean data

Data-Driven Transport Geometry for Rare Events in Metastable Systems

Tree-Based Pursuit

On the exponential convergence of Matching Pursuits in quasi-incoherent dictionaries

Conditional Deep Learning Model Reveals Translation Elongation Determinants during Amino Acid Deprivation

Progressive coding of 3D objects based on overcomplete decompositions

Cascade of Descriptors to Detect and Track Objects Across Any Network of Cameras

Situational Awareness Using A Single Omnidirectional Camera

Image compression with learnt tree-structured dictionaries

Localization of Sound Sources in a Room with One Microphone

Atoms of all channels, unite! Average case analysis of multi-channel sparse recovery using greedy algorithms

Spread Spectrum for Universal Compressive Sampling

Nonnegative Matrix Factorization and Spatial Covariance Model for Under-Determined Reverberant Audio Source Separation

Robust Principal Component Analysis on Graphs

Very low bit rate image coding using redundant dictionaries

Light Field Compressive Sensing in Camera Arrays

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

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

Image reconstruction of non-planar scenes from compressed multi-view measurements

Towards improving full-length ribosome density prediction by bridging sequence and graph-based representations