Wideband Super-resolution Imaging in Radio Interferometry via Low Rankness and Joint Average Sparsity Models (HyperSARA)

We propose a new approach within the versatile framework of convex optimization to solve the radio-interferometric wideband imaging problem. Our approach, dubbed HyperSARA, solves a sequence of weighted nuclear norm and l21 minimization problems promoting low rankness and joint average sparsity of the wideband model cube. On the one hand, enforcing low rankness enhances the overall resolution of the reconstructed model cube by exploiting the correlation between the different channels. On the other hand, promoting joint average sparsity improves the overall sensitivity by rejecting artefacts present on the different channels. An adaptive Preconditioned Primal-Dual algorithm is adopted to solve the minimization problem. The algorithmic structure is highly scalable to large data sets and allows for imaging in the presence of unknown noise levels and calibration errors. We showcase the superior performance of the proposed approach, reflected in high-resolution images on simulations and real VLA observations with respect to single channel imaging and the CLEAN-based wideband imaging algorithm in the WSCLEAN software. Our MATLAB code is available online on GITHUB

Déconvolution d'images en radioastronomie centimétrique pour l'exploitation des nouveaux interféromètres radio : caractérisation du milieu non thermique des amas de galaxies

Within the framework of the preparation for the Square Kilometre Array (SKA), that is the world largest radio telescope, new imaging challenges has to be conquered. The data acquired by SKA will have to be processed on real time because of their huge rate. In addition, thanks to its unprecedented resolution and sensitivity, SKA images will have very high dynamic range over wide fields of view. Hence, there is an urgent need for the design of new imaging techniques that are robust and efficient and fully automated. The goal of this thesis is to develop a new technique aiming to reconstruct a model image of the radio sky from the radio observations. The method have been designed to estimate images with high dynamic range with a particular attention to recover faint extended emission usually completely buried in the PSF sidelobes of the brighter sources and the noise. We propose a new approach, based on sparse representations, called MORESANE. The radio sky is assumed to be a summation of sources, considered as atoms of an unknown synthesis dictionary. These atoms are learned using analysis priors from the observed image. Results obtained on realistic simulations show that MORESANE is very promising in the restoration of radio images; it is outperforming the standard tools and very competitive with the newly proposed methods in the literature. MORESANE is also applied on simulations of observations using the SKA1 with the aim to investigate the detectability of the intracluster non thermal component. Our results indicate that these diffuse sources, characterized by very low surface brightness will be investigated up to the epoch of massive cluster formation with the SKA.Dans le cadre de la préparation du Square Kilometre Array (SKA), le plus large radio interféromètre au monde, de nouveaux défis de traitement d'images sont à relever. En effet, les données fournies par SKA auront un débit énorme, nécessitant ainsi un traitement en temps réel. En outre, grâce à sa résolution et sa sensibilité sans précédent, les observations seront dotées d'une très forte dynamique sur des champs de vue très grands. De nouvelles méthodes de traitement d'images robustes, efficaces et automatisées sont alors exigées. L'objectif de la thèse consiste à développer une nouvelle méthode permettant la restauration du modèle de l'image du ciel à partir des observations. La méthode est conçue pour l'estimation des images de très forte dynamique avec une attention particulière à restaurer les émissions étendues et faibles en intensité, souvent noyées dans les lobes secondaires de la PSF et le bruit. L'approche proposée est basée sur les représentations parcimonieuses, nommée MORESANE. L'image du ciel est modélisée comme étant la superposition de sources, qui constitueront les atomes d'un dictionnaire de synthèse inconnu, ce dernier sera estimé par des a priori d'analyses. Les résultats obtenus sur des simulations réalistes montrent que MORESANE est plus performant que les outils standards et très compétitifs avec les méthodes récemment proposées dans la littérature. MORESANE est appliqué sur des simulations d'observations d'amas de galaxies avec SKA1 afin d'investiguer la détectabilité du milieu non thermique intra-amas. Nos résultats indiquent que cette émission, avec SKA, sera étudiée jusqu'à l'époque de la formation des amas de galaxies massifs

An accelerated splitting algorithm for radio-interferometric imaging: when natural and uniform weighting meet

Next generation radio-interferometers, like the Square Kilometre Array, will acquire tremendous amounts of data with the goal of improving the size and sensitivity of the reconstructed images by orders of magnitude. The efficient processing of large-scale data sets is of great importance. We propose an acceleration strategy for a recently proposed primal-dual distributed algorithm. A preconditioning approach can incorporate into the algorithmic structure both the sampling density of the measured visibilities and the noise statistics. Using the sampling density information greatly accelerates the convergence speed, especially for highly non-uniform sampling patterns, while relying on the correct noise statistics optimises the sensitivity of the reconstruction. In connection to CLEAN, our approach can be seen as including in the same algorithmic structure both natural and uniform weighting, thereby simultaneously optimising both the resolution and the sensitivity. The method relies on a new non-Euclidean proximity operator for the data fidelity term, that generalises the projection onto the $\ell_2$ ball where the noise lives for naturally weighted data, to the projection onto a generalised ellipsoid incorporating sampling density information through uniform weighting. Importantly, this non-Euclidean modification is only an acceleration strategy to solve the convex imaging problem with data fidelity dictated only by noise statistics. We showcase through simulations with realistic sampling patterns the acceleration obtained using the preconditioning. We also investigate the algorithm performance for the reconstruction of the 3C129 radio galaxy from real visibilities and compare with multi-scale CLEAN, showing better sensitivity and resolution. Our MATLAB code is available online on GitHub

Cygnus A super-resolved via convex optimisation from VLA data

We leverage the Sparsity Averaging Reweighted Analysis (SARA) approach for interferometric imaging, that is based on convex optimisation, for the super-resolution of Cyg A from observations at the frequencies 8.422GHz and 6.678GHz with the Karl G. Jansky Very Large Array (VLA). The associated average sparsity and positivity priors enable image reconstruction beyond instrumental resolution. An adaptive Preconditioned Primal-Dual algorithmic structure is developed for imaging in the presence of unknown noise levels and calibration errors. We demonstrate the superior performance of the algorithm with respect to the conventional CLEAN-based methods, reflected in super-resolved images with high fidelity. The high resolution features of the recovered images are validated by referring to maps of Cyg A at higher frequencies, more precisely 17.324GHz and 14.252GHz. We also confirm the recent discovery of a radio transient in Cyg A, revealed in the recovered images of the investigated data sets. Our matlab code is available online on GitHub.Comment: 14 pages, 7 figures (3/7 animated figures), accepted for publication in MNRA

Scalable precision wide-field imaging in radio interferometry: I. uSARA validated on ASKAP data

As Part I of a paper series showcasing a new imaging framework, we consider the recently proposed unconstrained Sparsity Averaging Reweighted Analysis (uSARA) optimisation algorithm for wide-field, high-resolution, high-dynamic range, monochromatic intensity imaging. We reconstruct images from real radio-interferometric observations obtained with the Australian Square Kilometre Array Pathfinder (ASKAP) and present these results in comparison to the widely-used, state-of-the-art imager WSClean. Selected fields come from the ASKAP Early Science and Evolutionary Map of the Universe (EMU) Pilot surveys and contain several complex radio sources: the merging cluster system Abell 3391-95, the merging cluster SPT-CL 2023-5535, and many extended, or bent-tail, radio galaxies, including the X-shaped radio galaxy PKS 2014-558 and the ``dancing ghosts'', known collectively as PKS 2130-538. The modern framework behind uSARA utilises parallelisation and automation to solve for the w-effect and efficiently compute the measurement operator, allowing for wide-field reconstruction over the full field-of-view of individual ASKAP beams (up to 3.3 deg each). The precision capability of uSARA produces images with both super-resolution and enhanced sensitivity to diffuse components, surpassing traditional CLEAN algorithms which typically require a compromise between such yields. Our resulting monochromatic uSARA-ASKAP images of the selected data highlight both extended, diffuse emission and compact, filamentary emission at very high resolution (up to 2.2 arcsec), revealing never-before-seen structure. Here we present a validation of our uSARA-ASKAP images by comparing the morphology of reconstructed sources, measurements of diffuse flux, and spectral index maps with those obtained from images made with WSClean.Comment: Accepted for publication in MNRA

Scalable precision wide-field imaging in radio interferometry: II. AIRI validated on ASKAP data

Accompanying Part I, this sequel delineates a validation of the recently proposed AI for Regularisation in radio-interferometric Imaging (AIRI) algorithm on observations from the Australian Square Kilometre Array Pathfinder (ASKAP). The monochromatic AIRI-ASKAP images showcased in this work are formed using the same parallelised and automated imaging framework described in Part I: ``uSARA validated on ASKAP data''. Using a Plug-and-Play approach, AIRI differs from uSARA by substituting a trained denoising deep neural network (DNN) for the proximal operator in the regularisation step of the forward-backward algorithm during deconvolution. We build a trained shelf of DNN denoisers which target the estimated image-dynamic-ranges of our selected data. Furthermore, we quantify variations of AIRI reconstructions when selecting the nearest DNN on the shelf versus using a universal DNN with the highest dynamic range, opening the door to a more complete framework that not only delivers image estimation but also quantifies epistemic model uncertainty. We continue our comparative analysis of source structure, diffuse flux measurements, and spectral index maps of selected target sources as imaged by AIRI and the algorithms in Part I -- uSARA and WSClean. Overall we see an improvement over uSARA and WSClean in the reconstruction of diffuse components in AIRI images. The scientific potential delivered by AIRI is evident in further imaging precision, more accurate spectral index maps, and a significant acceleration in deconvolution time, whereby AIRI is four times faster than its sub-iterative sparsity-based counterpart uSARA.Comment: Accepted for publication in MNRA

MORESANE: MOdel REconstruction by Synthesis-ANalysis Estimators. A sparse deconvolution algorithm for radio interferometric imaging

(arXiv abridged abstract) The current years are seeing huge developments of radio telescopes and a tremendous increase of their capabilities. Such systems make mandatory the design of more sophisticated techniques not only for transporting, storing and processing this new generation of radio interferometric data, but also for restoring the astrophysical information contained in such data. In this paper we present a new radio deconvolution algorithm named MORESANE and its application to fully realistic simulated data of MeerKAT, one of the SKA precursors. This method has been designed for the difficult case of restoring diffuse astronomical sources which are faint in brightness, complex in morphology and possibly buried in the dirty beam's side lobes of bright radio sources in the field. MORESANE is a greedy algorithm which combines complementary types of sparse recovery methods in order to reconstruct the most appropriate sky model from observed radio visibilities. A synthesis approach is used for the reconstruction of images, in which the synthesis atoms representing the unknown sources are learned using analysis priors. We apply this new deconvolution method to fully realistic simulations of radio observations of a galaxy cluster and of an HII region in M31. We show that MORESANE is able to efficiently reconstruct images composed from a wide variety of sources from radio interferometric data. Comparisons with other available algorithms, which include multi-scale CLEAN and the recently proposed methods by Li et al. (2011) and Carrillo et al. (2012), indicate that MORESANE provides competitive results in terms of both total flux/surface brightness conservation and fidelity of the reconstructed model. MORESANE seems particularly well suited for the recovery of diffuse and extended sources, as well as bright and compact radio sources known to be hosted in galaxy clusters.Comment: 17 pages, 11 figures, accepted for publication on A&

Robust dimensionality reduction for interferometric imaging of Cygnus A

Extremely high data rates expected in next-generation radio interferometers necessitate a fast and robust way to process measurements in a big data context. Dimensionality reduction can alleviate computational load needed to process these data, in terms of both computing speed and memory usage. In this article, we present image reconstruction results from highly reduced radio-interferometric data, following our previously proposed data dimensionality reduction method, Rsing, based on studying the distribution of the singular values of the measurement operator. This method comprises a simple weighted, subsampled discrete Fourier transform of the dirty image. Additionally, we show that an alternative gridding-based reduction method works well for target data sizes of the same order as the image size. We reconstruct images from well-calibrated VLA data to showcase the robustness of our proposed method down to very low data sizes in a 'real data' setting. We show through comparisons with the conventional reduction method of time- and frequency-averaging, that our proposed method produces more accurate reconstructions while reducing data size much further, and is particularly robust when data sizes are aggressively reduced to low fractions of the image size. Rsing can function in a block-wise fashion, and could be used in the future to process incoming data by blocks in real-time, thus opening up the possibility of performing 'on-line' imaging as the data are being acquired. MATLAB code for the proposed dimensionality reduction method is available on GitHub