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Pierre Vandergheynst

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Publications associées (216)

Average case analysis of sparse recovery with Thresholding: New bounds based on average dictionary coherence

Pierre Vandergheynst, Mohammad Golbabaee

This paper analyzes the performance of the simple thresholding algorithm for sparse signal representations. In particular, in order to be more realistic we introduce a new probabilistic signal model which assumes randomness for both the amplitude and also ...

2008

Non-Gaussianity analysis on local morphological measures of WMAP data

Pierre Vandergheynst, Yves Wiaux

The decomposition of a signal on the sphere with the steerable wavelet constructed from the second Gaussian derivative gives access to the orientation, signed-intensity and elongation of the signal’s local features. In the present work, the non-Gaussianity ...

2008

Dictionary Learning Based Dimensionality Reduction for Classification

Pierre Vandergheynst, Karin Schnass

In this article we present a signal model for classification based on a low dimensional dictionary embedded into the high dimensional signal space. We develop an alternate projection algorithm to find the embedding and the dictionary and finally test the c ...

2008

Probing dark energy with steerable wavelets through correlation of WMAP and NVSS local morphological measures

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

Using local morphological measures on the sphere defined through a steerable wavelet analysis, we examine the three-year WMAP and the NVSS data for correlation induced by the integrated Sachs-Wolfe (ISW) effect. The steerable wavelet constructed from the s ...

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

On the estimation of geodesic paths on sampled manifolds under random projections

Pierre Vandergheynst, Matteo Sorci

In this paper, we focus on the use of random projections as a dimensionality reduction tool for sampled manifolds in high-dimensional Euclidean spaces. We show that geodesic paths approximations from nearest neighbors Euclidean distances are well-preserved ...

2008

Shape from Texture for Omnidirectional Images

Pierre Vandergheynst, Eugenio De Vito, Luigi Bagnato, Laurent Jacques

In this paper, we describe a method to infer 3-D scene information using a single view captured by an omnidirectional camera. The proposed technique is inscribed in the so called ``Shape from Texture'' problem : if the textures hold by 3-D surfaces respect ...

2008

Exact reconstruction with directional wavelets on the sphere

Pierre Vandergheynst, Yves Wiaux, Jason Douglas McEwen

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of a previously developed wavelet formalism developed by Antoine & Vandergheynst and Wiaux et a ...

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

The continuous wavelet transform on conic sections

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give s ...

2008

Dictionary preconditioning for greedy algorithms

Pierre Vandergheynst, Karin Schnass

This article presents an alteration of greedy algorithms like thresholding or (Orthogonal) Matching Pursuit which improves their performance in finding sparse signal representations in redundant dictionaries. These algorithms can be split into a sensing an ...

2008

Compressed sensing and redundant dictionaries

Pierre Vandergheynst, Karin Schnass

This article extends the concept of it compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic ...

2008

On finding approximate nearest neighbours in a set of compressible signals

Philippe Jost, Pierre Vandergheynst

Numerous applications demand that we manipulate large sets of very high-dimensional signals. A simple yet common example is the problem of finding those signals in a database that are closest to a query. In this paper, we tackle this problem by restricting ...

2008

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

Fast spin +-2 spherical harmonics transforms and application in cosmology

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness of the transform ...

2007

Scale-space analysis and active contours for omnidirectional images

Jean-Philippe Thiran, Pierre Vandergheynst, Iva Bogdanova Vandergheynst, Xavier Bresson

A new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras, namely catadioptric cameras, is slowly emerging. These omnidirectional images will most probably deeply impact computer vision i ...

Institute of Electrical and Electronics Engineers2007

On finding nearest neighbors in a set of compressible signals

Philippe Jost, Pierre Vandergheynst

2007

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

Tracking Atoms with Particles for Audio-visual Source Localization

Andrea Cavallaro, Pierre Vandergheynst, Gianluca Monaci, Emilio Maggio

We present a general framework and an efficient algorithm for tracking relevant video structures. The structures to be tracked are implicitly defined by a Matching Pursuit procedure that extracts and ranks the most important image contours. Based on the ra ...

2007

Matching Pursuit with Block Incoherent Dictionaries

Pierre Vandergheynst, Lorenzo Peotta

There has been an intense activity recently in the field of sparse approximations with redundant dictionaries, largely motivated by the practical performances of algorithms such as Matching Pursuit and Basis Pursuit. However, most of the theoretical result ...

2007

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