Jason Douglas McEwen

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The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of the most powerfu ...

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 ...

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 ...

We propose a novel regularization method for compressive imaging in the context of the CS theory with coherent and redundant dictionaries. The approach relies on the conjecture that natural images exhibit strong average sparsity over multiple coherent fram ...

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 ...

Recent developments in [1] and [2] introduced a novel regularization method for compressive imaging in the con- text of compressed sensing with coherent redundant dictionaries. The approach relies on the observation that natural images exhibit strong avera ...

In the general context of complex data processing, this paper reviews a recent practical approach to the continuous wavelet formalism on the sphere. This formalism notably yields a correspondence principle which relates wavelets on the plane and on the sph ...

We study the impact of the spread spectrum effect in radio interferometry on the quality of image reconstruction. This spread spectrum effect will be induced by the wide ﬁeld-of-view of forthcoming radio interferometric telescopes. The resulting chirp modu ...

We describe S2LET, a fast and robust implementation of the scale-discretised wavelet transform on the sphere. Wavelets are con- structed through a tiling of the harmonic line and can be used to probe spatially localised, scale-depended features of signals ...

We propose a transform for signals defined on the sphere that reveals their localized directional content in the spatio-spectral domain when used in conjunction with an asymmetric window function. We call this transform the directional spatially localized ...

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 m ...

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 ...

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 ...

We review scale-discretized wavelets on the sphere, which are directional and allow one to probe oriented struc- ture in data defined on the sphere. Furthermore, scale-discretized wavelets allow in practice the exact synthesis of a signal from its wavelet ...

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 ...

Incorporating wide-field considerations in interferometric imaging is of increasing importance for next-generation radio telescopes. Compressed sensing techniques for interferometric imaging have been extended to wide fields recently, recovering images in ...

A new sampling theorem on the sphere has been developed recently, reducing the number of samples required to represent a band-limited signal by a factor of two for equiangular sampling schemes. For signals sparse in a spatially localised measure, such as i ...

For the next generation of radio interferometric telescopes it is of paramount importance to incorporate wide field-of-view (WFOV) considerations in interferometric imaging, otherwise the fidelity of reconstructed images will suffer greatly. We extend comp ...

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 ban ...

We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit strong average sparsity over multiple coherent frames. W ...

Jason Douglas McEwen

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Cosmological applications of a wavelet analysis on the sphere

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

Exact reconstruction with directional wavelets on the sphere

Sparsity averaging for radio-interferometric imaging

Compressed sensing for radio interferometric imaging: review and future

On Sparsity Averaging

Complex data processing: fast wavelet analysis on the sphere

The varying w spread spectrum effect for radio interferometric imaging

S2LET: A code to perform fast wavelet analysis on the sphere

Fast Directional Spatially Localized Spherical Harmonic Transform

PURIFY: a new approach to radio-interferometric imaging

Data compression on the sphere

Sampling theorems and compressive sensing on the sphere

On the computation of directional scale-discretized wavelet transforms on the sphere

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

Intrinsic advantages of the w component and spherical imaging for wide-field radio interferometry

Sparse image reconstruction on the sphere: implications of a new sampling theorem

Compressed sensing for wide-field radio interferometric imaging

A novel sampling theorem on the sphere

Sparsity Averaging for Compressive Imaging