Next-generation radio interferometers, such as the Square Kilometre Array (SKA), will revolutionise our understanding of the universe through their unprecedented sensitivity and resolution. However, to realise these goals significant challenges in image and data processing need to be overcome. The standard methods in radio interferometry for reconstructing images, such as CLEAN, have served the community well over the last few decades and have survived largely because they are pragmatic. However, they produce reconstructed inter\-ferometric images that are limited in quality and scalability for big data. In this work we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software package. In particular, we implement and apply the proximal alternating direction method of multipliers (P-ADMM) algorithm presented in a recent article. First, we assess the impact of the interpolation kernel used to perform gridding and degridding on sparse image reconstruction. We find that the Kaiser-Bessel interpolation kernel performs as well as prolate spheroidal wave functions, while providing a computational saving and an analytic form. Second, we apply PURIFY to real interferometric observations from the Very Large Array (VLA) and the Australia Telescope Compact Array (ATCA) and find images recovered by PURIFY are higher quality than those recovered by CLEAN. Third, we discuss how PURIFY reconstructions exhibit additional advantages over those recovered by CLEAN. The latest version of PURIFY, with developments presented in this work, is made publicly available.
Next-generation radio interferometers, such as the Square Kilometre Array (SKA), will revolutionise our understanding of the universe through their unprecedented sensitivity and resolution. However, standard methods in radio interferometry produce reconstructed interferometric images that are limited in quality and they are not scalable for big data. In this work we apply and evaluate alternative interferometric reconstruction methods that make use of state-of-the-art sparse image reconstruction algorithms motivated by compressive sensing, which have been implemented in the PURIFY software pac…
In recent works, compressed sensing (CS) and convex optimization techniques have been applied to radio-interferometric imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. We review our latest contributions, which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted in a new software PURIFY (beta version) relies on the simulta…
In recent works, sparse models and convex optimization techniques have been applied to radio-interferometric (RI) imaging showing the potential to outperform state-of-the-art imaging algorithms in the field. In this talk, I will review our latest contributions in RI imaging, which leverage the versatility of convex optimization to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to high-dimensional data scalability. Firstly, I will review our recently proposed average sparsity approach, SARA, which relies on the observation that natural i…
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 simulations in a simple discrete visibility setting, to have the potential to outperform significantly CLEAN and its evolutions. In this work, we leverage the versatility of convex optimization in solving minimization problems to both handle realistic…
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 algor…
We present a new algorithm to perform wide-field radio interferometric image reconstruction, with exact non-coplanar correction, that scales to big-data. This algorithm allows us to image 2 billion visibilities on 50 nodes of a computing cluster for a 25 by 25 degree field of view, in a little over an hour. We build on the recently developed distributed $w$-stacking $w$-projection hybrid algorithm, extending it to include a new distributed degridding algorithm that balances the computational load of the $w$-projection gridding kernels. The implementation of our algorithm is made publicly avail…
The concept of a recently proposed small-scale interferometric optical imaging device, an instrument known as the Segmented Planar Imaging Detector for Electro-optical Reconnaissance (SPIDER), is of great interest for its possible applications in astronomy and space science. Due to low weight, low power consumption, and high resolution, the SPIDER telescope could replace the large space telescopes that exist today. Unlike traditional optical interferometry the SPIDER accurately retrieves both phase and amplitude information, making the measurement process analogous to a radio interferometer. S…
Compressed sensing theory is slowly making its way to solve more and more astronomical inverse problems. We address here the application of sparse representations, convex optimization and proximal theory to radio interferometric imaging. First, we expose the theory behind interferometric imaging, sparse representations and convex optimization, and second, we illustrate their application with numerical tests with SASIR, an implementation of the FISTA, a Forward-Backward splitting algorithm hosted in a LOFAR imager. Various tests have been conducted in Garsden et al., 2015. The main results are:…
We develop a novel algorithm for sparse Stokes parameters imaging in radio interferometry under the polarization constraint. The latter is a physical non-linear relation between the Stokes parameters, imposing that the polarization intensity is a lower bound on the total intensity. To solve the joint inverse Stokes imaging problem including this bound, we leverage epigraphical projection techniques in convex optimization and design a primal-dual method offering a highly flexible and parallelizable structure. In addition, we propose to regularize each Stokes parameter map through an average spa…
The standard wide-field imaging technique, the $w$-projection, allows correction for wide-fields of view for non-coplanar radio interferometric arrays. However, calculating exact corrections for each measurement has not been possible due to the amount of computation required at high resolution and with the large number of visibilities from current interferometers. The required accuracy and computational cost of these corrections is one of the largest unsolved challenges facing next generation radio interferometers such as the Square Kilometre Array. We show that the same calculation can be per…
Modern radio telescopes, such as the Square Kilometre Array (SKA), will probe the radio sky over large fields-of-view, which results in large w-modulations of the sky image. This effect complicates the relationship between the measured visibilities and the image under scrutiny. In algorithmic terms, it gives rise to massive memory and computational time requirements. Yet, it can be a blessing in terms of reconstruction quality of the sky image. In recent years, several works have shown that large w-modulations promote the spread spectrum effect. Within the compressive sensing framework, this e…
(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 d…
Next-generation radio interferometric telescopes will exhibit non-coplanar baseline configurations and wide field-of-views, inducing a w-modulation of the sky image, which in turn induces the spread spectrum effect. We revisit the impact of this effect on imaging quality and study a new algorithmic strategy to deal with the associated operator in the image reconstruction process. In previous studies it has been shown that image recovery in the framework of compressed sensing is improved due to the spread spectrum effect, where the w-modulation can act to increase the incoherence between measur…
Despite image reconstruction becoming more widespread when interpreting OIFITS Data, model fitting in u,v space often remains the best way to interpret data, either because of the sparsity of the data, or because a quantitative measurement needs to be done. PMOIRED, is a flexible Python library to visualize, manipulate and model OIFITS data using simple geometric models. The strength of PMOIRED resides in its capability to combine linearly various simple components to create complex scenes, while linking, constraining, and adding priors to fitted parameters. The code also enables grid search t…
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier samples of the sky. However, these imagers assumes a steady sky and the complexity of the problem increases when transients radio sources are also present in the data. Hopefully, in the context of transient imaging, the spatial and temporal information are separable which enable extension of an imager fit for a steady sky. We introduce independent spatial and tem…
Interferometric measurements of the radio emission of extensive air showers allow reconstructing cosmic-ray properties. A recent simulation study with an idealised detector promised measurements of the depth of the shower maximum $X_\mathrm{max}$ with an accuracy better than 10$\,$g$\,$cm$^{-2}$. In this contribution, we evaluate the potential of interferometric $X_\mathrm{max}$ measurements of (simulated) inclined air showers with realistically dimensioned, sparse antenna arrays. We account for imperfect time synchronisation between individual antennas and study its inter-dependency with the …
The analysis of astronomical interferometric data is often performed on the images obtained after deconvolution of the interferometer's point spread function (PSF). This strategy can be understood (especially for cases of sparse arrays) as fitting models to models, since the deconvolved images are already non-unique model representations of the actual data (i.e., the visibilities). Indeed, the interferometric images may be affected by visibility gridding, weighting schemes (e.g., natural vs. uniform), and the particulars of the (non-linear) deconvolution algorithms. Fitting models to the direc…
This paper provides a general introduction to the problem of image reconstruction from interferometric data. A simple model of the interferometric observables is given and the issues arising from sparse Fourier data are discussed. The effects of various regularizations are described. In the proposed general framework, most existing algorithms can be understood. For an astronomer, such an understanding is crucial not only for selecting and using an algorithm but also to ensure correct interpretation of the resulting image.
Interferometric measurements with arrays of radio antennas are a powerful and widely used technique in astronomy. Recently, this technique has been revisited for the reconstruction of extensive air showers [1]. This radio-interferometric technique exploits the coherence in the radio emission emitted by billions of secondary shower particles to reconstruct the shower parameters, in particular the shower axis and depth of the shower maximum $X_\mathrm{max}$. The accuracy previously demonstrated on simulations with an idealized detector is very promising. In this article we evaluate the potential…
We propose a new superresolution imaging technique for interferometry using sparse modeling, utilizing two regularization terms: the $\ell_1$-norm and a new function named Total Squared Variation (TSV) of the brightness distribution. TSV is an edge-smoothing variant of Total Variation (TV), leading to reducing the sum of squared gradients. First, we demonstrate that our technique may achieve super-resolution of $\sim 30$% compared to the traditional CLEAN beam size using synthetic observations of two point sources. Second, we present simulated observations of three physically motivated static …
Compressing radio interferometric visibility data into a probabilistic model using sparse Gaussian processes
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙物理数学研究所（WPI））；Center for Data-Driven Discovery, Kavli IPMU (WPI), UTIAS, The University of Tokyo（东京大学数据驱动发现中心，Kavli IPMU（WPI），UTIAS）
Sub-milliarcsecond imaging of nearby main sequence stars and binary systems can provide critical information on stellar phenomena such as rotational deformation, accretion effects, and the universality of starspot (sunspot) cycles. Achieving this level of resolution in optical wavelength bands (U/V) requires use of a sparse array of interferometric telescopes with kilometer scale baseline separations. Current ground based VHE gamma-ray observatories, such as VERITAS, HESS, and MAGIC, employ arrays of > 10 m diameter optical Imaging Atmospheric Cherenkov Telescopes (IACTs) with >80 m telescope …
We propose a new technique to obtain super-resolution images with radio interferometer using sparse modeling. In standard radio interferometry, sampling of ($u$, $v$) is quite often incomplete and thus obtaining an image from observed visibilities becomes an underdetermined problem, and a technique so-called "zero-padding" is often used to fill up unsampled grids in ($u$, $v$) plane, resulting in image degradation by finite beam size as well as numerous side-lobes. In this paper we show that directly solving such an underdetermined problem based on sparse modeling (in this paper LASSO) avoids …
Uncertainty quantification is a critical missing component in radio interferometric imaging that will only become increasingly important as the big-data era of radio interferometry emerges. Since radio interferometric imaging requires solving a high-dimensional, ill-posed inverse problem, uncertainty quantification is difficult but also critical to the accurate scientific interpretation of radio observations. Statistical sampling approaches to perform Bayesian inference, like Markov Chain Monte Carlo (MCMC) sampling, can in principle recover the full posterior distribution of the image, from w…
We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurements of the string signal, which exhibits sparse or compressible magnitude of the gradient due to the Kaiser-Stebbins (KS) effect. In this context the versatile framework of compressed sensing naturally applies for solving the corresponding inverse problem. Our algorithm notably takes advantage of a model of the prior statistical distribution of…
The sparse interferometric coverage of the Event Horizon Telescope (EHT) poses a significant challenge for both reconstruction and model fitting of black-hole images. PRIMO is a new principal components analysis-based algorithm for image reconstruction that uses the results of high-fidelity general relativistic, magnetohydrodynamic simulations of low-luminosity accretion flows as a training set. This allows the reconstruction of images that are both consistent with the interferometric data and that live in the space of images that is spanned by the simulations. PRIMO follows Monte Carlo Markov…
We introduce a new Markov Chain Monte Carlo (MCMC) algorithm with parallel tempering for fitting theoretical models of horizon-scale images of black holes to the interferometric data from the Event Horizon Telescope (EHT). The algorithm implements forms of the noise distribution in the data that are accurate for all signal-to-noise ratios. In addition to being trivially parallelizable, the algorithm is optimized for high performance, achieving 1 million MCMC chain steps in under 20 seconds on a single processor. We use synthetic data for the 2017 EHT coverage of M87 that are generated based on…
Interferometric imaging now achieves angular resolutions as fine as 10 microarcsec, probing scales that are inaccessible to single telescopes. Traditional synthesis imaging methods require calibrated visibilities; however, interferometric calibration is challenging, especially at high frequencies. Nevertheless, most studies present only a single image of their data after a process of "self-calibration," an iterative procedure where the initial image and calibration assumptions can significantly influence the final image. We present a method for efficient interferometric imaging directly using …
The emerging generation of radio interferometric (RI) telescopes, such as the Square Kilometre Array (SKA), will acquire massive volumes of data and transition radio astronomy to a big-data era. The ill-posed inverse problem of imaging the raw visibilities acquired by RI telescopes will become significantly more computationally challenging, particularly in terms of data storage and computational cost. Current RI imaging methods, such as CLEAN, its variants, and compressive sensing approaches (sparse regularisation), have yielded excellent reconstruction fidelity. However, scaling these methods…
The Event Horizon Telescope image of the supermassive black hole in the galaxy M87 is dominated by a bright, unresolved ring. General relativity predicts that embedded within this image lies a thin "photon ring," which is composed of an infinite sequence of self-similar subrings that are indexed by the number of photon orbits around the black hole. The subrings approach the edge of the black hole "shadow," becoming exponentially narrower but weaker with increasing orbit number, with seemingly negligible contributions from high order subrings. Here, we show that these subrings produce strong an…
Reconstructing images from very long baseline interferometry (VLBI) data with sparse sampling of the Fourier domain (uv-coverage) constitutes an ill-posed deconvolution problem. It requires application of robust algorithms maximizing the information extraction from all of the sampled spatial scales and minimizing the influence of the unsampled scales on image quality. We develop a new multiscale wavelet deconvolution algorithm DoG-HiT for imaging sparsely sampled interferometric data which combines the difference of Gaussian (DoG) wavelets and hard image thresholding (HiT). Based on DoG-HiT, w…
Context. The LOw Frequency ARray (LOFAR) radio telescope is a giant digital phased array interferometer with multiple antennas distributed in Europe. It provides discrete sets of Fourier components of the sky brightness. Recovering the original brightness distribution with aperture synthesis forms an inverse problem that can be solved by various deconvolution and minimization methods Aims. Recent papers have established a clear link between the discrete nature of radio interferometry measurement and the "compressed sensing" (CS) theory, which supports sparse reconstruction methods to form an i…
Massachusetts Institute of Technology（麻省理工学院）；Harvard-Smithsonian Center for Astrophysics（哈佛-史密森天体物理中心）；Massachusetts General Hospital（麻省总医院）；Radboud University（拉德堡德大学）；Google Research（谷歌研究院）
Very long baseline interferometry (VLBI) makes it possible to recover images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wavelengths with a goal of achieving angular resolution sufficient for imaging the event horizons of nearby supermassive black holes. VLBI provides measurements related to the underlying source image through a sparse set spatial frequencies. An image can then be recovered from these measurements by making assumptions about the underlying image. One of the most important…
With an emphasis on improving the fidelity even in super-resolution regimes, new imaging techniques have been intensively developed over the last several years, which may provide substantial improvements to the interferometric observation of protoplanetary disks. In this study, sparse modeling (SpM) is applied for the first time to observational data sets taken by the Atacama Large Millimeter/submillimeter Array (ALMA). The two data sets used in this study were taken independently using different array configurations at Band 7 (330 GHz), targeting the protoplanetary disk around HD 142527; one …
SIFARI: Self-Supervised Interferometric Fitting for Astronomical Radio Imaging
Rice University（莱斯大学）；Rice Space Institute（莱斯空间研究所）；National Radio Astronomy Observatory（美国国家射电天文台）；NSF-Simons AI Institute for Cosmic Origins（NSF-西蒙斯宇宙起源人工智能研究所）；University of Pennsylvania（宾夕法尼亚大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
We propose a new technique for radio interferometry to obtain super-resolution full polarization images in all four Stokes parameters using sparse modeling. The proposed technique reconstructs the image in each Stokes parameter from the corresponding full-complex Stokes visibilities by utilizing two regularization functions: the $\ell _1$-norm and total variation (TV) of the brightness distribution. As an application of this technique, we present simulated linear polarization observations of two physically motivated models of M87 with the Event Horizon Telescope (EHT). We confirm that $\ell _1…
Modern interferometric imaging relies on advanced calibration that incorporates direction-dependent effects. Their increasing number of antennas (e.g. in LOFAR, VLA, MeerKAT/SKA) and sensitivity are often tempered with the accuracy of their calibration. Beam accuracy drives particularly the capability for high dynamic range imaging (HDR - contrast > 1:$10^6$). The Radio Interferometric Measurement Equation (RIME) proposes a refined calibration framework for wide field of views (i.e. beyond the primary lobe and first null) using beam models. We have used holography data taken on 12 antennas of …
We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show mathematically that the Fourier transforms of eigenimages derived from PCA applied to an ensemble of images in the spatial-domain are identical to the eigenvectors of PCA applied to the ensemble of the Fourier transforms of the images, which suggests that this approach may be applied to modeling the sparse interferometric Fourier-visibilities produced by an array such as…
A Non-Negativity Iterative Approach to Image Deconvolution for SKA
School of Physics and Astronomy, Sun Yat-sen University（中山大学物理与天文学院）；CSST Science Center for the Guangdong-Hong Kong-Macau Greater Bay Area（粤港澳大湾区宇宙大尺度结构与星系中心科学中心）
Sparse aperture masking interferometry (SAM) is a high resolution observing technique that allows for imaging at and beyond a telescope's diffraction limit. The technique is ideal for searching for stellar companions at small separations from their host star; however, previous analysis of SAM observations of young stars surrounded by dusty disks have had difficulties disentangling planet and extended disk emission. We analyse VLT/SPHERE-IRDIS SAM observations of the transition disk LkCa\,15, model the extended disk emission, probe for planets at small separations, and improve contrast limits f…
By linking widely separated radio dishes, the technique of very long baseline interferometry (VLBI) can greatly enhance angular resolution in radio astronomy. However, at any given moment, a VLBI array only sparsely samples the information necessary to form an image. Conventional imaging techniques partially overcome this limitation by making the assumption that the observed cosmic source structure does not evolve over the duration of an observation, which enables VLBI networks to accumulate information as the Earth rotates and changes the projected array geometry. Although this assumption is …
Radio Frequency Interference (RFI) is an ever-present limiting factor among radio telescopes even in the most remote observing locations. When looking to retain the maximum amount of sensitivity and reduce contamination for Epoch of Reionization studies, the identification and removal of RFI is especially important. In addition to improved RFI identification, we must also take into account computational efficiency of the RFI-Identification algorithm as radio interferometer arrays such as the Hydrogen Epoch of Reionization Array grow larger in number of receivers. To address this, we present a …
Generating images from very long baseline interferometric observations poses a difficult, and generally not unique, inversion problem. This problem is simplified by the introduction of constraints, some generic (e.g., positivity of the intensity) and others motivated by physical considerations (e.g., smoothness, instrument resolution). It is further complicated by the need to simultaneously address instrumental systematic uncertainties and sparse coverage in the u-v plane. We report a new Bayesian image reconstruction technique in the parameter estimation framework Themis that has been develop…
