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Yves Wiaux

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Related publications (88)

Sampling theorems and compressive sensing on the sphere

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Yves Wiaux, Gilles Puy, Jason Douglas McEwen

We discuss a novel sampling theorem on the sphere developed by McEwen & Wiaux recently through an association between the sphere and the torus. To represent a band-limited signal exactly, this new sampling theorem requires less than half the number of samp ...

Spie-Int Soc Optical Engineering, Po Box 10, Bellingham, Wa 98227-0010 Usa2011

Spread Spectrum for Universal Compressive Sampling

Pierre Vandergheynst, Yves Wiaux, Rémi Gribonval, Gilles Puy

We propose a universal and efficient compressive sampling strategy based on the use of a spread spectrum technique. The method essentially consists in a random pre-modulation of the signal of interest followed by projections onto randomly selected vectors ...

2011

Matching Pursuit Iterative Dipole Based Filter of Background Fields in Phase Imaging

Rolf Gruetter, Yves Wiaux, José Pedro Rebelo Ferreira Marques

The information present in the phase of gradient-echo images has opened a new window to look at fine brain anatomy. To obtain high quality phase images depicting small field perturbations produced by tissue susceptibility differences, large slowly spatiall ...

2011

On Variable Density Compressive Sampling

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution provides an optimize ...

IEEE Institute of Electrical and Electronics Engineers2011

Implications for compressed sensing of a new sampling theorem on the sphere

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Yves Wiaux, Gilles Puy, Jason Douglas McEwen

A sampling theorem on the sphere has been developed recently, requiring half as many samples as alternative equiangular sampling theorems on the sphere. A reduction by a factor of two in the number of samples required to represent a band-limited signal on ...

2011

Data compression on the sphere

Yves Wiaux, Jason Douglas McEwen

Large data-sets defined on the sphere arise in many fields. In particular, recent and forthcoming observations of the anisotropies of the cosmic microwave background (CMB) made on the celestial sphere contain approximately three and fifty mega-pixels respe ...

Indian Academy of Sciences2011

Accelerated MR imaging with spread spectrum encoding

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Rolf Gruetter, Yves Wiaux, José Pedro Rebelo Ferreira Marques, Gilles Puy

We advocate the use of a novel compressed sensing technique for accelerating the magnetic resonance image acquisition process, coined spread spectrum MR imaging or simply s2MRI. The method resides in pre-modulating the signal of interest by a linear chirp, ...

2011

Compressed sensing for radio interferometric imaging: review and future

Yves Wiaux, Jason Douglas McEwen

Radio interferometry is a powerful technique for astronomical imaging. The theory of compressed sensing (CS) has been applied recently to the ill-posed inverse problem of recovering images from the measurements taken by radio interferometric telescopes. We ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011

Harmonic analysis of spherical sampling in diffusion MRI

Jean-Philippe Thiran, Dimitri Nestor Alice Van De Ville, Yves Wiaux, Alessandro Daducci, Jason Douglas McEwen

In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of effectively mapping th ...

2011

Spread spectrum for interferometric and magnetic resonance imaging

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Rolf Gruetter, Yves Wiaux, Gilles Puy

We consider images probed through incomplete and noisy Fourier coverages, both in the context of radio interferometry (RI) and of magnetic resonance imaging (MRI). We show that the quality of signal reconstruction can be signiﬁcantly enhanced by the introd ...

IEEE Signal Process. Soc.2010

Spread spectrum for compressed sensing techniques in magnetic resonance imaging

Jean-Philippe Thiran, Pierre Vandergheynst, Dimitri Nestor Alice Van De Ville, Rolf Gruetter, Yves Wiaux, Gilles Puy

Magnetic resonance imaging (MRI) probes signals through Fourier measurements. Accelerating the acquisition process is of major interest for various MRI applications. The recent theory of compressed sensing shows that sparse or compressible signals may be r ...

IEEE Signal Process. Soc.2010

Compressed sensing reconstruction of a string signal from interferometric observations of the cosmic microwave background

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurement ...

Wiley-Blackwell2010

Compressed sensing for radio interferometry: prior-enhanced Basis Pursuit imaging techniques

Pierre Vandergheynst, Yves Wiaux, Gilles Puy, Laurent Jacques

We propose and assess the performance of new imaging techniques for radio interferometry that rely on the versatility of the compressed sensing framework to account for prior information on the signals. The present manuscript represents a summary of recent ...

2009

Wavelet domain Bayesian denoising of string signal in the cosmic microwave background

Pierre Vandergheynst, Yves Wiaux

An algorithm is proposed for denoising the signal induced by cosmic strings in the cosmic microwave background (CMB). A Bayesian approach is taken, based on modeling the string signal in the wavelet domain with generalized Gaussian distributions. Good perf ...

2009

Compressed sensing for radio interferometry: spread spectrum imaging techniques

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We consider the problem of reconstruction of astrophysical signals probed by radio interferometers with baselines bearing a non-negligible component in the pointing direction. The visibilities measured essentially identify with a noisy and incomplete Fouri ...

2009

Spread spectrum for imaging techniques in radio interferometry

Pierre Vandergheynst, Yves Wiaux, Gilles Puy

We consider the probe of astrophysical signals through radio interferometers with small field of view and baselines with non-negligible and constant component in the pointing direction. In this context, the visibilities measured essentially identify with a ...

Wiley-Blackwell2009

Compressed sensing imaging techniques for radio interferometry

Pierre Vandergheynst, Yves Wiaux, Gilles Puy, Laurent Jacques

Radio interferometry probes astrophysical signals through incomplete and noisy Fourier measurements. The theory of compressed sensing demonstrates that such measurements may actually suffice for accurate reconstruction of sparse or compressible signals. We ...

Wiley-Blackwell2009

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

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

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

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