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Pierre Vandergheynst

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Publications associées (216)

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

Blind Audiovisual Source Separation Using Sparse Representations

Pierre Vandergheynst, Gianluca Monaci, Anna Llagostera Casanovas

In this work we present a method to jointly separate active audio and visual structures on a given mixture. Blind Audiovisual Source Separation is achieved exploiting the coherence between a video signal and a one-microphone audio track. The efficient repr ...

2007

Average Performance Analysis for Thresholding

Pierre Vandergheynst, Karin Schnass

In this article is shown that with high probability the thresholding algorithm can recover signals that are sparse in a redundant dictionary as long as the {\it 2-Babel function} is growing slowly. This implies that it can succeed for sparsity levels up to ...

IEEE Institute of Electrical and Electronics Engineers2007

Wavelets on the two-sphere and other conic sections

Pierre Vandergheynst

We review the construction of the continuous wavelet transform (CWT) on the two-sphere by two methods, the group-theoretical approach and the geometrical method based on conformal invariance. Then we discuss the discretization of the spherical CWT, obtaini ...

2007

Alignment and signed-intensity anomalies in WMAP data

Pierre Vandergheynst, Yves Wiaux

Significant alignment and signed-intensity anomalies of local features of the cosmic microwave background (CMB) are detected on the three-year WMAP data, through a decomposition of the signal with steerable wavelets on the sphere. In addition to identifyin ...

2007

Fast Global Minimization of the Active Contour/Snake Model

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson

The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numeri ...

2007

Continuous Wavelet Transform on the Hyperboloid

Pierre Vandergheynst, Iva Bogdanova Vandergheynst

In this paper we build a Continuous Wavelet Transform (CWT) on the upper sheet of the 2-hyperboloid

H_+^2

. First, we define a class of suitable dilations on the hyperboloid through conic projection. Then, incorporating hyperbolic motions belonging to $SO ...

2007

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

Progressive Coding of 3-D Objects Based on Overcomplete Decompositions

Pascal Frossard, Pierre Vandergheynst, Ivana Tosic

This paper presents a progressive coding scheme for 3-D objects, based on overcomplete signal expansions on the 2-D sphere. Due to increased freedom in the basis construction, redundant expansions have shown interesting approximation properties in the deco ...

2006

Audiovisual Gestalts

Pierre Vandergheynst, Gianluca Monaci

This paper presents an algorithm to correlate audio and visual data generated by the same physical phenomenon. According to psychophysical experiments, temporal synchrony strongly contributes to integrate cross-modal information in humans. Thus, we define ...

2006

Distributed coding of Highly correlated image sequences with motion-compensated temporal wavelets

Pierre Vandergheynst

This paper discusses robust coding of visual content for a distributed multimedia system. The system encodes independently two correlated video signals and reconstructs them jointly at a central decoder. The video signals are captured from a dynamic scene ...

2006

Analysis of Multimodal Sequences Using Geometric Video Representations

Pierre Vandergheynst, Oscar Divorra Escoda, Gianluca Monaci

This paper presents a novel method to correlate audio and visual data generated by the same physical phenomenon, based on sparse geometric representation of video sequences. The video signal is modeled as a sum of geometric primitives evolving through time ...

2006

Low rate and flexible image coding with redundant representations

Pascal Frossard, Pierre Vandergheynst

New breakthroughs in image coding possibly rely in signal decomposition through non-separable basis functions. The work proposed in this paper provides an adaptive way of representing images as a sum of two-dimensional features. It presents a low bit-rate ...

2006

Distributed sensing of noisy signals by thresholding of redundant expansions

Pascal Frossard, Pierre Vandergheynst, Karin Schnass

This paper addresses the problem of sensing or recovering a signal s, captured by distributed low-complexity sensors. Each sensor observes a noisy version of the signal of interest, and independently forms an approximant of its observation. This approximan ...

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

Multiscale Active Contours

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson

We propose a new multiscale image segmentation model, based on the active contour/snake model and the Polyakov action. The concept of scale, general issue in physics and signal processing, is introduced in the active contour model, which is a well-known im ...

2006

A Variational Model for Object Segmentation Using Boundary Information and Shape Prior Driven by the Mumford-Shah Functional

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson

In this paper, we propose a new variational model to segment an object belonging to a given shape space using the active contour method, a geometric shape prior and the Mumford-Shah functional. The core of our model is an energy functional composed by thre ...

Springer, Kluwer Academic Publishers2006

Ventricular and Atrial Activity Estimation Through Sparse ECG Signal Decompositions

Jean-Marc Vesin, Pierre Vandergheynst, Oscar Divorra Escoda, Lorenzo Granai, Mathieu Lemay

This paper explores a novel approach for ventricular and atrial activities estimation in electrocardiogram (ECG) signals, based on sparse source separation. Sparse decompositions of ECG over signal-adapted multi-component dictionaries can lead to natural s ...

2006

Global universe anisotropy probed by the alignment of structures in the cosmic microwave background

Pierre Vandergheynst, Yves Wiaux

We question the global universe isotropy by probing the alignment of local structures in the cosmic microwave background (CMB) radiation. The original method proposed relies on a steerable wavelet decomposition of the CMB signal on the sphere. The analysis ...

2006

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