In this paper we consider the problem of sampling far below the Nyquist rate signals that are sparse linear superpositions of shifts of a known, potentially wide-band, pulse. This signal model is key for applications such as Ultra Wide Band (UWB) communica ...

2009

A low complexity orthogonal matching pursuit for sparse signal approximation with shift-invariant dictionaries

Pierre Vandergheynst, Rémi Gribonval

We propose a variant of Orthogonal Matching Pursuit (OMP), called LoCOMP, for scalable sparse signal approximation. The algorithm is designed for shift- invariant signal dictionaries with localized atoms, such as time-frequency dictionaries, and achieves a ...

2009

Dictionary learning for the sparse modelling of atrial fibrillation in ECG signals

Jean-Marc Vesin, Pierre Vandergheynst, Rémi Gribonval

We propose a new method for ventricular cancellation and atrial modelling in the ECG of patients suffering from atrial fibrillation. Our method is based on dictionary learning. It extends both the average beat subtraction and the sparse source separation a ...

2009

Some Recovery Conditions for Basis Learning by L1-Minimization

Karin Schnass, Rémi Gribonval

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

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

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

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

Blind Audiovisual Separation based on Redundant Representations

Pierre Vandergheynst, Gianluca Monaci, Rémi Gribonval, 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

Dictionary Identifiability from Few Training Samples

Karin Schnass, Rémi Gribonval

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

Learning Multi-Modal Dictionaries

Philippe Jost, Pierre Vandergheynst, Gianluca Monaci, Rémi Gribonval

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

Multichannel thresholding with sensing dictionaries

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

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 thresholding

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

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

Average case analysis of multichannel sparse approximations using p- thresholding

Pierre Vandergheynst, Karin Schnass, Rémi Gribonval

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

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 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

MoTIF: An Efficient Algorithm for Learning Translation Invariant Dictionaries

Philippe Jost, Pierre Vandergheynst, Rémi Gribonval

The performances of approximation using redundant expansions rely on having dictionaries adapted to the signals. In natural high-dimensional data, the statistical dependencies are, most of the time, not obvious. Learning fundamental patterns is an alternat ...

2006

Learning Multi-Modal Dictionaries: Application to Audiovisual Data

Philippe Jost, Pierre Vandergheynst, Gianluca Monaci, Rémi Gribonval

This paper presents a methodology for extracting meaningful synchronous structures from multi-modal signals. Simultaneous processing of multi-modal data can reveal information that is unavailable when handling the sources separately. However, in natural hi ...

2006

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

Page 2 sur 2