Publications by Rémi Gribonval

Blind Audiovisual Separation based on Redundant Representations

Pierre Vandergheynst, Rémi Gribonval, Gianluca Monaci, Anna Llagostera Casanovas

In this work we present a method to perform a complete audiovisual source separation without need of previous information. This method is based on the assumption that sounds are caused by moving structures. Thus, an efficient representation of audio and vi ...

2008

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

Dictionary Identifiability from Few Training 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, or more precisely the problem of identifying a dictionary

dico

from a set of training samples

Y

knowing that $ ...

2008

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

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 graph. We define a notion of scaling using the graph analogue of the Fourier domain, namely the space of eigenfunctions forming the sp ...

2008

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

Average case analysis of multichannel sparse approximations using p- thresholding

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

This paper introduces

p

-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latte ...

2007

Multichannel thresholding with sensing dictionaries

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

This paper shows introduces the use sensing dictionaries for p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We do both a worst case and average case recovery analyses of this ...

2007

Average case analysis of multichannel sparse approximations using p-thresholding - art. no. 67011X

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

This paper introduces p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latter ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2007

Average case analysis of multichannel thresholding

Pierre Vandergheynst, Rémi Gribonval, Karin Schnass

This paper introduces p-thresholding, an algorithm to compute simultaneous sparse approximations of multichannel signals over redundant dictionaries. We work out both worst case and average case recovery analyses of this algorithm and show that the latter ...

2007

Rémi Gribonval

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Blind Audiovisual Separation based on Redundant Representations

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

Dictionary Identifiability from Few Training Samples

Some Recovery Conditions for Basis Learning by L1-Minimization

Wavelets on Graphs via Spectral Graph Theory

Learning Multi-Modal Dictionaries

Average case analysis of multichannel sparse approximations using p- thresholding

Multichannel thresholding with sensing dictionaries

Average case analysis of multichannel sparse approximations using p-thresholding - art. no. 67011X

Average case analysis of multichannel thresholding

Blind Audiovisual Separation based on Redundant Representations

Dictionary Identifiability from Few Training Samples

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

Wavelets on Graphs via Spectral Graph Theory

Multichannel thresholding with sensing dictionaries

Some Recovery Conditions for Basis Learning by L1-Minimization

Average case analysis of multichannel sparse approximations using p- thresholding

Average case analysis of multichannel thresholding

Learning Multi-Modal Dictionaries

Average case analysis of multichannel sparse approximations using p-thresholding - art. no. 67011X