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Pierre Vandergheynst

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Publications associées (216)

Image compression using an edge adapted redundant dictionary and wavelets

Pierre Vandergheynst, Lorenzo Peotta, Lorenzo Granai

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 ...

2006

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

Steerable wavelet analysis of CMB structures alignment

Pierre Vandergheynst, Yves Wiaux

This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering of the CMB sign ...

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

Fast directional correlation on the sphere with steerable filters

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

A fast algorithm is developed for the directional correlation of scalar band-limited signals and band-limited steerable filters on the sphere. The asymptotic complexity associated to it through simple quadrature is of order O(L^5), where 2L stands for the ...

2006

Flexible Motion-Adaptive Video Coding with Redundant Expansions

Pascal Frossard, Pierre Vandergheynst, Adel Rahmoune

This paper presents a highly flexible video coding scheme (MP3D), based on the use of a redundant 3-D spatio-temporal dictionary of functions. Directionality and anisotropic scaling are key ingredients to the spatial components, that form a rich collection ...

2006

On the Use of A Priori Information for Sparse Signal Approximations

Pierre Vandergheynst, Oscar Divorra Escoda, Lorenzo Granai

Recent results have underlined the importance of incoherence in redundant dictionaries for a good behavior of decomposition algorithms like Matching and Basis Pursuits. However, appropriate dictionaries for a given application may not necessarily be able t ...

2006

Coarse-to-fine textures retrieval in the JPEG 2000 compressed domain for fast browsing of large image databases

Pierre Vandergheynst, Benoît Macq, Christophe De Vleeschouwer

In many applications, the amount and resolution of digital images have significantly increased over the past few years. For this reason, there is a growing interest for techniques allowing to efficiently browse and seek information inside such huge data sp ...

2006

Tree-Based Pursuit: Algorithm and Properties

Pascal Frossard, Philippe Jost, Pierre Vandergheynst

This paper proposes a tree-based pursuit algorithm that efficiently trades off complexity and approximation performance for overcomplete signal expansions. Finding the sparsest representation of a signal using a redundant dictionary is, in general, a NP-Ha ...

2006

Matching pursuit-based shape representation and recognition using scale-space

François Mendels, Jean-Philippe Thiran, Pierre Vandergheynst

In this paper, we propose an analytical low-level representation of images, obtained by a decomposition process, namely the matching pursuit (MP) algorithm, as a new way of describing objects through a general continuous description using an affine invaria ...

2006

Processor Enhancements for Media Streaming Applications

Eric Debes, Pierre Vandergheynst, Sébastien Bilavarn

The development of more processing demanding applications on the Internet (video broadcasting) on one hand and the popularity of recent devices at the user level (digital cameras, wireless videophones, ...) on the other hand introduce challenges at several ...

Springer, Kluwer Academic Publishers2005

Correspondence principle between spherical and Euclidean wavelets

Pierre Vandergheynst, Yves Wiaux, Laurent Jacques

Wavelets on the sphere are reintroduced and further developed independently of the original group theoretic formalism, in an equivalent, but more straightforward approach. These developments are motivated by the interest of the scale-space analysis of the ...

2005

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

Stereographic Wavelet Frames on the Sphere

Pierre Vandergheynst, Iva Bogdanova Vandergheynst, Laurent Jacques

In this paper we exploit the Continuous Wavelet Transform (CWT) on the two dimensional sphere, introduced previously by two of us, to build associated Discrete Wavelet Frames. We first explore half-continuous frames, i.e., frames where the position remains ...

2005

An Improved Pyramid for Spatially Scalable Video Coding

Pierre Vandergheynst

This paper discusses an improved pyramid for spatially scalable video coding. We introduce additional update steps in the analysis and the synthesis of the Laplacian pyramid. Our pyramid is able to control efficiently the quantization noise energy in the r ...

2005

Minimiseurs Globaux du Modele des Contours Actifs

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Leila Cammoun

Le modele des contours actifs [6,2,7] est un des modeles variationnels de segmentation les plus connus en traitement d'images. Cependant, ce modele est limite par l'existence de minima locaux qui rend la condition initiale critique pour obtenir des resulta ...

2005

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