#### Filter Results:

- Full text PDF available (93)

#### Publication Year

1999

2017

- This year (6)
- Last 5 years (62)
- Last 10 years (93)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Brain Region

#### Cell Type

#### Key Phrases

#### Method

#### Organism

Learn More

- Jason D. McEwen, Yves Wiaux
- IEEE Transactions on Signal Processing
- 2011

We develop a novel sampling theorem on the sphere and corresponding fast algorithms by associating the sphere with the torus through a periodic extension. The fundamental property of any sampling theorem is the number of samples required to represent a band-limited signal. To represent exactly a signal on the sphere band-limited at <i>L</i>, all sampling… (More)

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 propose new generic imaging techniques based on convex optimization for global minimization problems… (More)

- Yves Wiaux
- 2008

Wavelets on the sphere are re-introduced and further developed independently of the original group theoretic formalism, in an alternative and completely equivalent approach, as inverse stereographic projection of wavelets on the plane. These developments are motivated by the interest of the scale-space analysis of the cosmic microwave background (CMB)… (More)

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 the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined… (More)

We propose a novel algorithm for image reconstruction in radio interferometry. The ill-posed inverse problem associated with the incomplete Fourier sampling identified by the visibility measurements is regularized by the assumption of average signal sparsity over representations in multiple wavelet bases. The algorithm, defined in the versatile framework of… (More)

- Yves Wiaux
- 2006

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(L5), where 2L stands for the square-root of the number of sampling points on the sphere, also setting a band limit L for the signals… (More)

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a minimization problem for image reconstruction. This approach was shown, in theory and through… (More)

- Gilles Puy, José P. Marques, +4 authors Yves Wiaux
- IEEE Trans. Med. Imaging
- 2012

We propose a novel compressed sensing technique to accelerate the magnetic resonance imaging (MRI) acquisition process. The method, coined spread spectrum MRI or simply s(2)MRI, consists of premodulating the signal of interest by a linear chirp before random k-space under-sampling, and then reconstructing the signal with nonlinear algorithms that promote… (More)

- Mike E. Davies, Gilles Puy, Pierre Vandergheynst, Yves Wiaux
- SIAM J. Imaging Sciences
- 2014

Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF) technique, we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the… (More)

- Gilles Puy, Pierre Vandergheynst, Rémi Gribonval, Yves Wiaux
- EURASIP J. Adv. Sig. Proc.
- 2012

We advocate a compressed sensing strategy that consists of multiplying the signal of interest by a wide bandwidth modulation before projection onto randomly selected vectors of an orthonormal basis. First, in a digital setting with random modulation, considering a whole class of sensing bases including the Fourier basis, we prove that the technique is… (More)