Project

Discipline

Signal processing: matrix completion; SKA: Square Kilometre array; Signal processing: inverse problems; Astronomy: radio interferometry; Astronomy: imaging; Signal processing: sparsity; Astronomy: calibration; Signal processing: compressive sampling

Lead
Les défis scientifiques pour les décennies à venir en astronomie requièrent que les futurs radio-interféromètres permettent l'imagerie de phénomènes beaucoup plus ténus qu'aujourd'hui, et à plus haute résolution angulaire. Ces télescopes devront prendre en compte des données hyperspectrales et polarisées, sur de larges champs de vue, et surmonter de nouveaux problèmes de calibration. Dans ce conttexte, les techniques d'imagerie par interférométrie doivent tout simplement être réinventées.
Lay summary
Le présent projet a pour objectif de produire des avancées conceptuelles et algorithmiques pour l'imagerie hyperspectrale et la calibration de données en radio-interférométrie, reposant sur la nouvelle théorie de l'échantillonnage compressif. Cette théorie  démontre qu'il est possible de reconstruire des signaux parcimonieux à partir de données incomplètes, et propose de nouvelles techniques d'acquisition et de reconstruction de tels signaux. Nous démontrerons les avantages de cette approche, tant en termes de la qualité des images produites qu'en termes de la rapidité de la reconstruction et la possibilité de traiter des images de grande dimension. Une comparaison approfondie de nos développements avec l'état de l'art sera réalisée, et un logiciel sera fourni pour utilisation indépendante par les radioastronomes.

Direct link to Lay Summary

Last update: 18.07.2013

Active participation

Self-organised

Number	Title	Start	Funding scheme

Aperture synthesis in radio interferometry is a powerful technique that dates back to more than sixty years ago. It allows observations of the sky with otherwise inaccessible angular resolutions and sensitivities (i.e. dynamic range), providing a wealth of information for astrophysics and cosmology. The measurement equation for aperture synthesis provides incomplete linear information about the signal, thus defining an ill-posed inverse problem in the perspective of signal reconstruction. Under restrictive assumptions of narrow-band (i.e. monochromatic) non-polarized imaging on small fields of view, the visibilities measured identify with Fourier measurements. Already powerful calibration and imaging techniques have been developed in the field, which in essence regularize the inverse problem through an implicit sparsity assumption of the signal in the spatial dimensions.The new science envisaged for the next decades in astronomy requires that next-generation radio telescopes, such as the new LOw Frequency ARray (LOFAR), or the future Extended Very Large Array (EVLA) and Square Kilometer Array (SKA), achieve much higher dynamic range than current instruments, also at higher angular resolution. These telescopes will also have to consider wide-band (i.e. hyper-spectral) polarized imaging on wide fields of view on the celestial sphere. Direction-dependent effects further complicate the measurement equation, and will have to be accounted for in this high-dimensional imaging process, and calibrated. In this context, calibration and imaging techniques for radio interferometry literally need to be re-invented, thus triggering an intense research in the field.The now famous theory of compressive sampling deals with the recovery of sparse signals from incomplete linear measurements. It acknowledges the fact that natural signals often exhibit a sparse representation in multi-scale bases, and proposes both optimization of the acquisition techniques, and a large variety of regularization priors to solve an ill-posed inverse problem for image reconstruction, in particular through convex optimization. Dr Wiaux and Prof. Thiran are renowned experts in signal processing, in particular compressive sampling. Dr Wiaux pioneered the field of compressive sampling for radio interferometry, as evident from his publications and the subsequent work triggered in the radio interferometry community.A first 2-year project of the Swiss National Science Foundation (SNSF) conducted by Dr Wiaux in the context of compressive sampling for radio interferometry, and that ended in July 2012, provided advances in the design of fast image reconstruction algorithms improving imaging relatively to state-of-the-art techniques, also tackling wide-field considerations. A second ongoing 1-year SNSF project of Dr Wiaux ending in July 2013 is dedicated to imaging in the presence of direction-dependent effects in a realistic setting, in particular accounting for continuous measurement distributions, still in a wide-field setting. This second project also aims at delivering a beta version of a novel imaging software, dubbed PURIFY, to the radio astronomy community.The present 3-year PhD project aims at continuing the ongoing project by providing conceptual and technical (i.e. programming) advances, still in a wide-field setting, for wide-band imaging on one side, and calibration of direction-dependent effects on the other side. Beyond standard compressive sampling ideas for promoting signal sparsity, these advances will rely on the theory of matrix completion, one of the latest evolutions in the field compressive sampling, dealing with the recovery of low-rank matrices, i.e. sparse in their singular value decomposition, from incomplete linear measurements. Wide-band signals or calibration matrices bear a non-negligible degree of structure or correlation and thus represent very interesting targets.We will demonstrate the advantage in speed and versatility of convex optimization algorithms for wide-band wide-field imaging and calibration, enabling both enhanced signal reconstruction quality and scalability to high-dimensional problems, in the perspective of LOFAR and SKA. A potentially paradigm-shifting data reduction approach, based on the concept of dimension embedding so fundamental to compressive sampling, will also be investigated to further accelerate processing and optimise memory requirements of our algorithms. A tight comparison of our developments with the state-of-the-art calibration and imaging techniques will be performed and a stable version of our software PURIFY, that should enable wide-band wide-field calibration and imaging, will finally be released for independent use by radio astronomers.This proposal thus reinforces a unique attempt at the international level to bridge the gaps between compressive sampling and aperture synthesis in radio interferometry. As such, and as suggested by the recognized expertise of the applicants, it will significantly advance the state-of-the-art calibration and imaging techniques in radio interferometry, thereby enhancing the quality of astrophysical and cosmological interpretation of the data.