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Rémi Gribonval

Cette personne a quitté l’EPFL

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Publications associées (37)

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Some Recovery Conditions for Basis Learning by L1-Minimization

Rémi Gribonval, Karin Schnass

Many recent works have shown that if a given signal admits a sufficiently sparse representation in a given dictionary, then this representation is recovered by several standard optimization algorithms, in particular the convex

\ell^1

minimization approac ...

2008

Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques

Pierre Vandergheynst, Yves Wiaux, Rémi Gribonval, Gilles Puy

We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. Firstly, in a digital setting with random modulation, con ...

Institute of Electrical and Electronics Engineers2012

Dictionary Identification - Sparse Matrix-Factorisation via $\ell_1$-Minimisation

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

\ell_1

-minimisation. The problem can also be seen as factorising a

\ddim \times \nsig

matrix $Y=(y_1 \ldots y_\nsig), , y_n\in \R^\ ...

Institute of Electrical and Electronics Engineers2010

Wavelets on graphs via spectral graph theory

Pierre Vandergheynst, Rémi Gribonval

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 ...

Elsevier2011

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

Pierre Vandergheynst, Rémi Gribonval

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 ...

2006

A Wideband Doubly-Sparse Approach For MITO Sparse Filter Estimation

Rémi Gribonval

We propose an approach for the estimation of sparse filters from a convolutive mixture of sources, exploiting the time-domain sparsity of the mixing filters and the sparsity of the sources in the time-frequency (TF) domain. The proposed approach is based o ...

IEEE2011

Learning Multi-Modal Dictionaries

Pierre Vandergheynst, Rémi Gribonval, Gianluca Monaci, Philippe Jost

Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This par ...

2007

A simple test to check the optimality of sparse signal approximations

Pierre Vandergheynst, Rémi Gribonval

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 ...

2005

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

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

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 ...

2008

Convex Optimization Approaches for Blind Sensor Calibration using Sparsity

Rémi Gribonval, Gilles Puy

We investigate a compressive sensing framework in which the sensors introduce a distortion to the measurements in the form of unknown gains. We focus on blind calibration, using measures performed on multiple unknown (but sparse) signals and formulate the ...

Institute of Electrical and Electronics Engineers2014

A Tractable Framework for Estimating and Combining Spectral Source Models for Audio Source Separation

Rémi Gribonval

The underdetermined blind audio source separation (BSS) problem is often addressed in the time-frequency (TF) domain assuming that each TF point is modeled as an independent random variable with sparse distribution. On the other hand, methods based on stru ...

2012

Compressive Spectral Clustering

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy

Spectral clustering has become a popular technique due to its high performance in many contexts. It comprises three main steps: create a similarity graph between N objects to cluster, compute the first k eigenvectors of its Laplacian matrix to define a fea ...

2016

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

Pierre Vandergheynst, Rémi Gribonval

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 ...

2006

MULAN: A Blind and Off-Grid Method for Multichannel Echo Retrieval

Rémi Gribonval, Helena Peic Tukuljac

This paper addresses the general problem of blind echo retrieval, i.e., given M sensors measuring in the discrete-time domain M mixtures of K delayed and attenuated copies of an unknown source signal, can the echo locations and weights be recovered? This p ...

2018

Basis Identification from Random Sparse Samples

Rémi Gribonval, Karin Schnass

This article treats the problem of learning a dictionary providing sparse representations for a given signal class, via

\ell_1

minimisation. The problem is to identify a dictionary

\dico

from a set of training samples

\Y

knowing that

\Y = \dico \X

...

2009

Spread Spectrum for Universal Compressive Sampling

Pierre Vandergheynst, Yves Wiaux, Rémi Gribonval, Gilles Puy

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 ...

2011

Double Sparsity: Towards Blind Estimation of Multiple Channels

Rémi Gribonval

We propose a framework for blind multiple filter estimation from convolutive mixtures, exploiting the time-domain sparsity of the mixing filters and the disjointness of the sources in the time-frequency domain. The proposed framework includes two steps: (a ...

Springer-Verlag's2010

Random sampling of bandlimited signals on graphs

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy

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, i.e., independent of the graph structure, and its performa ...

Elsevier2018

Blind Phase Calibration in Sparse Recovery

Rémi Gribonval, Gilles Puy

We consider a blind calibration problem in a compressed sensing measurement system in which each sensor introduces an unknown phase shift to be determined. We show that this problem can be approached similarly to the problem of phase retrieval from quadrat ...

2013

Accelerated Spectral Clustering Using Graph Filtering of Random Signals

Pierre Vandergheynst, Rémi Gribonval, Gilles Puy

We build upon recent advances in graph signal processing to propose a faster spectral clustering algorithm. Indeed, classical spectral clustering is based on the computation of the first

k

eigenvectors of the similarity matrix' Laplacian, whose computati ...

Ieee2016