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

Distributed and parallel sparse convex optimization for radio interferometry with PURIFY

Next generation radio interferometric telescopes are entering an era of big data with extremely large data sets. While these telescopes can observe the sky in higher sensitivity and resolution than before, computational challenges in image reconstruction need to be overcome to realize the potential of forthcoming telescopes. New methods in sparse image reconstruction and convex optimization techniques (cf. compressive sensing) have shown to produce higher fidelity reconstructions of simulations and real observations than traditional methods. This article presents distributed and parallel algorithms and implementations to perform sparse image reconstruction, with significant practical considerations that are important for implementing these algorithms for Big Data. We benchmark the algorithms presented, showing that they are considerably faster than their serial equivalents. We then pre-sample gridding kernels to scale the distributed algorithms to larger data sizes, showing application times for 1 Gb to 2.4 Tb data sets over 25 to 100 nodes for up to 50 billion visibilities, and find that the run-times for the distributed algorithms range from 100 milliseconds to 3 minutes per iteration. This work presents an important step in working towards computationally scalable and efficient algorithms and implementations that are needed to image observations of both extended and compact sources from next generation radio interferometers such as the SKA. The algorithms are implemented in the latest versions of the SOPT (https://github.com/astro-informatics/sopt) and PURIFY (https://github.com/astro-informatics/purify) software packages {(Versions 3.1.0)}, which have been released alongside of this article.Comment: 25 pages, 5 figure

Multi-frequency image reconstruction for radio-interferometry with self-tuned regularization parameters

As the world's largest radio telescope, the Square Kilometer Array (SKA) will provide radio interferometric data with unprecedented detail. Image reconstruction algorithms for radio interferometry are challenged to scale well with TeraByte image sizes never seen before. In this work, we investigate one such 3D image reconstruction algorithm known as MUFFIN (MUlti-Frequency image reconstruction For radio INterferometry). In particular, we focus on the challenging task of automatically finding the optimal regularization parameter values. In practice, finding the regularization parameters using classical grid search is computationally intensive and nontrivial due to the lack of ground- truth. We adopt a greedy strategy where, at each iteration, the optimal parameters are found by minimizing the predicted Stein unbiased risk estimate (PSURE). The proposed self-tuned version of MUFFIN involves parallel and computationally efficient steps, and scales well with large- scale data. Finally, numerical results on a 3D image are presented to showcase the performance of the proposed approach

Imaging and uncertainty quantification in radio astronomy via convex optimization : when precision meets scalability

Upcoming radio telescopes such as the Square Kilometre Array (SKA) will provide sheer amounts of data, allowing large images of the sky to be reconstructed at an unprecedented resolution and sensitivity over thousands of frequency channels. In this regard, wideband radio-interferometric imaging consists in recovering a 3D image of the sky from incomplete and noisy Fourier data, that is a highly ill-posed inverse problem. To regularize the inverse problem, advanced prior image models need to be tailored. Moreover, the underlying algorithms should be highly parallelized to scale with the vast data volumes provided and the Petabyte image cubes to be reconstructed for SKA. The research developed in this thesis leverages convex optimization techniques to achieve precise and scalable imaging for wideband radio interferometry and further assess the degree of confidence in particular 3D structures present in the reconstructed cube. In the context of image reconstruction, we propose a new approach that decomposes the image cube into regular spatio-spectral facets, each is associated with a sophisticated hybrid prior image model. The approach is formulated as an optimization problem with a multitude of facet-based regularization terms and block-specific data-fidelity terms. The underpinning algorithmic structure benefits from well-established convergence guarantees and exhibits interesting functionalities such as preconditioning to accelerate the convergence speed. Furthermore, it allows for parallel processing of all data blocks and image facets over a multiplicity of CPU cores, allowing the bottleneck induced by the size of the image and data cubes to be efficiently addressed via parallelization. The precision and scalability potential of the proposed approach are confirmed through the reconstruction of a 15 GB image cube of the Cyg A radio galaxy. In addition, we propose a new method that enables analyzing the degree of confidence in particular 3D structures appearing in the reconstructed cube. This analysis is crucial due to the high ill-posedness of the inverse problem. Besides, it can help in making scientific decisions on the structures under scrutiny (e.g., confirming the existence of a second black hole in the Cyg A galaxy). The proposed method is posed as an optimization problem and solved efficiently with a modern convex optimization algorithm with preconditioning and splitting functionalities. The simulation results showcase the potential of the proposed method to scale to big data regimes

Parallel faceted imaging in radio interferometry via proximal splitting (Faceted HyperSARA): when precision meets scalability

Upcoming radio interferometers are aiming to image the sky at new levels of resolution and sensitivity, with wide-band image cubes reaching close to the Petabyte scale for SKA. Modern proximal optimization algorithms have shown a potential to significantly outperform CLEAN thanks to their ability to inject complex image models to regularize the inverse problem for image formation from visibility data. They were also shown to be scalable to large data volumes thanks to a splitting functionality enabling the decomposition of data into blocks, for parallel processing of block-specific data-fidelity terms of the objective function. In this work, the splitting functionality is further exploited to decompose the image cube into spatio-spectral facets, and enable parallel processing of facet-specific regularization terms in the objective. The resulting Faceted HyperSARA algorithm is implemented in MATLAB (code available on GitHub). Simulation results on synthetic image cubes confirm that faceting can provide a major increase in scalability at no cost in imaging quality. A proof-of-concept reconstruction of a 15 GB image of Cyg A from 7.4 GB of VLA data, utilizing 496 CPU cores on a HPC system for 68 hours, confirms both scalability and a quantum jump in imaging quality from CLEAN. Assuming slow spectral slope of Cyg A, we also demonstrate that Faceted HyperSARA can be combined with a dimensionality reduction technique, enabling utilizing only 31 CPU cores for 142 hours to form the Cyg A image from the same data, while preserving reconstruction quality. Cyg A reconstructed cubes are available online

Radio Astronomy Image Reconstruction in the Big Data Era

Next generation radio interferometric telescopes pave the way for the future of radio astronomy with extremely wide-fields of view and precision polarimetry not possible at other optical wavelengths, with the required cost of image reconstruction. These instruments will be used to map large scale Galactic and extra-galactic structures at higher resolution and fidelity than ever before. However, radio astronomy has entered the era of big data, limiting the expected sensitivity and fidelity of the instruments due to the large amounts of data. New image reconstruction methods are critical to meet the data requirements needed to obtain new scientific discoveries in radio astronomy. To meet this need, this work takes traditional radio astronomical imaging and introduces new of state-of-the-art image reconstruction frameworks of sparse image reconstruction algorithms. The software package PURIFY, developed in this work, uses convex optimization algorithms (i.e. alternating direction method of multipliers) to solve for the reconstructed image. We design, implement, and apply distributed radio interferometric image reconstruction methods for the message passing interface (MPI), showing that PURIFY scales to big data image reconstruction on computing clusters. We design a distributed wide-field imaging algorithm for non-coplanar arrays, while providing new theoretical insights for wide-field imaging. It is shown that PURIFY’s methods provide higher dynamic range than traditional image reconstruction methods, providing a more accurate and detailed sky model for real observations. This sets the stage for state-of-the-art image reconstruction methods to be distributed and applied to next generation interferometric telescopes, where they can be used to meet big data challenges and to make new scientific discoveries in radio astronomy and astrophysics

Advanced sparse optimization algorithms for interferometric imaging inverse problems in astronomy

In the quest to produce images of the sky at unprecedented resolution with high sensitivity, new generation of astronomical interferometers have been designed. To meet the sensing capabilities of these instruments, techniques aiming to recover the sought images from the incompletely sampled Fourier domain measurements need to be reinvented. This goes hand-in-hand with the necessity to calibrate the measurement modulating unknown effects, which adversely affect the image quality, limiting its dynamic range. The contribution of this thesis consists in the development of advanced optimization techniques tailored to address these issues, ranging from radio interferometry (RI) to optical interferometry (OI). In the context of RI, we propose a novel convex optimization approach for full polarization imaging relying on sparsity-promoting regularizations. Unlike standard RI imaging algorithms, our method jointly solves for the Stokes images by enforcing the polarization constraint, which imposes a physical dependency between the images. These priors are shown to enhance the imaging quality via various performed numerical studies. The proposed imaging approach also benefits from its scalability to handle the huge amounts of data expected from the new instruments. When it comes to deal with the critical and challenging issues of the direction-dependent effects calibration, we further propose a non-convex optimization technique that unifies calibration and imaging steps in a global framework, in which we adapt the earlier developed imaging method for the imaging step. In contrast to existing RI calibration modalities, our method benefits from well-established convergence guarantees even in the non-convex setting considered in this work and its efficiency is demonstrated through several numerical experiments. Last but not least, inspired by the performance of these methodologies and drawing ideas from them, we aim to solve image recovery problem in OI that poses its own set of challenges primarily due to the partial loss of phase information. To this end, we propose a sparsity regularized non-convex optimization algorithm that is equipped with convergence guarantees and is adaptable to both monochromatic and hyperspectral OI imaging. We validate it by presenting the simulation results

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