Selective Dynamical Imaging of Interferometric Data
Joseph Farah, Peter Galison, Kazunori Akiyama, Katherine L. Bouman, Geoffrey C. Bower, Andrew Chael, Antonio Fuentes, José L. Gómez, Mareki Honma, Michael D. Jo… 展开作者
Joseph Farah, Peter Galison, Kazunori Akiyama, Katherine L. Bouman, Geoffrey C. Bower, Andrew Chael, Antonio Fuentes, José L. Gómez, Mareki Honma, Michael D. Johnson, Yutaro Kofuji, Daniel P. Marrone, Kotaro Moriyama, Ramesh Narayan, Dominic W. Pesce, Paul Tiede, Maciek Wielgus, Guang-Yao Zhao, The Event Horizon Telescope Collaboration
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20 pages, 14 figures, published in ApJL (2022), uploaded for open access
Recent developments in very long baseline interferometry (VLBI) have made it possible for the Event Horizon Telescope (EHT) to resolve the innermost accretion flows of the largest supermassive black holes on the sky. The sparse nature of the EHT's $(u, v)$-coverage presents a challenge when attempting to resolve highly time-variable sources. We demonstrate that the changing (u, v)-coverage of the EHT can contain regions of time over the course of a single observation that facilitate dynamical imaging. These optimal time regions typically have projected baseline distributions that are approximately angularly isotropic and radially homogeneous. We derive a metric of coverage quality based on baseline isotropy and density that is capable of ranking array configurations by their ability to produce accurate dynamical reconstructions. We compare this metric to existing metrics in the literature and investigate their utility by performing dynamical reconstructions on synthetic data from simulated EHT observations of sources with simple orbital variability. We then use these results to make recommendations for imaging the 2017 EHT Sgr A* data set.
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 review novel CS radio interferometric imaging techniques, both at the level of acquisition and reconstruction, and discuss their superior performance relative to traditional approaches. In order to remain as close to the theory of CS as possible, these techniques necessarily consider idealised interferometric configurations. To realise the e…
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 compressed sensing techniques for interferometric imaging to a WFOV and recover images in the spherical coordinate space in which they naturally live, eliminating any distorting projection. The effectiveness of the spread spectrum phenomenon, highlighted recently by one of the authors, is enhanced when going to a WFOV, while sparsity is promoted …
Radio astronomy is transitioning to a big-data era due to the emerging generation of radio interferometric (RI) telescopes, such as the Square Kilometre Array (SKA), which will acquire massive volumes of data. In this article we review methods proposed recently to resolve the ill-posed inverse problem of imaging the raw visibilities acquired by RI telescopes in the big-data scenario. We focus on the recently proposed online reconstruction method [4] and the considerable savings in data storage requirements and computational cost that it yields.
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…
The celebrated CLEAN algorithm has been the cornerstone of deconvolution algorithms in radio interferometry almost since its conception in the 1970s. For all its faults, CLEAN is remarkably fast, robust to calibration artefacts and in its ability to model point sources. We demonstrate how the same assumptions that afford CLEAN its speed can be used to accelerate more sophisticated deconvolution algorithms.
We present a detailed discussion of the implementation strategies for a recently developed $w$-stacking $w$-projection hybrid algorithm used to reconstruct wide-field interferometric images. In particular, we discuss the methodology used to deploy the algorithm efficiently on a supercomputer via use of a Message Passing Interface (MPI) $k$-means clustering technique to achieve efficient construction and application of non co-planar effects. Additionally, we show that the use of conjugate symmetry increases the algorithms performance by imaging an interferometric observation of Fornax A from th…
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:…
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…
We present the results of the fifth Interferometric Imaging Beauty Contest. The contest consists in blind imaging of test data sets derived from model sources and distributed in the OIFITS format. Two scenarios of imaging with CHARA/MIRC-6T were offered for reconstruction: imaging a T Tauri disc and imaging a spotted red supergiant. There were eight different teams competing this time: Monnier with the software package MACIM; Hofmann, Schertl and Weigelt with IRS; Thiébaut and Soulez with MiRA ; Young with BSMEM; Mary and Vannier with MIROIRS; Millour and Vannier with independent BSMEM and MiR…
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 modulation improves the quality of reconstructed interferometric images by increasing the incoherence of the measurement and sparsity dictionaries. We extend previous studies of this effect to consider the more realistic setting where the chirp modulation varies for each visibility measurement made by the telescope. In these first preliminary re…
Radio interferometers observe the Fourier space of the sky, at locations determined by the array geometry. Before a real space image is constructed by a Fourier transform, the data is weighted to improve the quality of reconstruction. Two criteria for calculation of weights are maximizing sensitivity and minimizing point spread function (PSF) sidelobe levels. In this paper, we propose a novel weighting scheme suitable for ultra deep imaging experiments. The proposed weighting scheme is used to maximize sensitivity while minimizing PSF sidelobe variation across frequency and multiple epochs. We…
We report on a broader evaluation of statistical bootstrap resampling methods as a tool for pixel-level calibration and imaging fidelity assessment in radio interferometry. Pixel-level imaging fidelity assessment is a challenging problem, important for the value it holds in robust scientific interpretation of interferometric images, enhancement of automated pipeline reduction systems needed to broaden the user community for these instruments, and understanding leadingedge direction-dependent calibration and imaging challenges for future telescopes such as the Square Kilometer Array. This new c…
We propose a novel algorithm for image reconstruction in radio interferometry. The ill-posed inverse problem associated with the incomplete Fourier sampling identified by the visibility measurements is regularized by the assumption of average signal sparsity over representations in multiple wavelet bases. The algorithm, defined in the versatile framework of convex optimization, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We show through simulations that the proposed approach outperforms state-of-the-art imaging methods in the field, which are based on the assumption of signal spar…
The data reduction procedure for radio interferometers can be viewed as a combined calibration and imaging problem. We present an algorithm that unifies cross-calibration, self-calibration, and imaging. Being a Bayesian method, that algorithm does not only calculate an estimate of the sky brightness distribution, but also provides an estimate of the joint uncertainty which entails both the uncertainty of the calibration and the one of the actual observation. The algorithm is formulated in the language of information field theory and uses Metric Gaussian Variational Inference (MGVI) as the unde…
We present the results of the fourth Optical/IR Interferometry Imaging Beauty Contest. The contest consists of blind imaging of test data sets derived from model sources and distributed in the OI-FITS format. The test data consists of spectral data sets on an object "observed" in the infrared with spectral resolution. There were 4 different algorithms competing this time: BSMEM the Bispectrum Maximum Entropy Method by Young, Baron & Buscher; RPR the Recursive Phase Reconstruction by Rengaswamy; SQUEEZE a Markov Chain Monte Carlo algorithm by Baron, Monnier & Kloppenborg; and, WISARD the Weak-p…
We describe and demonstrate a technique for correcting direction dependent artifacts due to asymmetries in antenna patterns and differences among antennas used in radio interoferometric imaging. The technique can correct images in all Stokes parameters I, Q, U and V and is shown with simulated data to reduce the level of artifacts to near the level of those from the basic imaging technique. The demonstrations use simulations of a mixed array of 13.5 and 15 m antennas with asymmetric patterns. The flux densities and spectral indices of the sources in a high dynamic range realistic simulated sky…
Radio interferometric imaging aims to estimate an unknown sky intensity image from degraded observations, acquired through an antenna array. In the theoretical case of a perfectly calibrated array, it has been shown that solving the corresponding imaging problem by iterative algorithms based on convex optimization and compressive sensing theory can be competitive with classical algorithms such as CLEAN. However, in practice, antenna-based gains are unknown and have to be calibrated. Future radio telescopes, such as the SKA, aim at improving imaging resolution and sensitivity by orders of magni…
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…
In this paper we present DMC, a model and associated tool for polarimetric imaging of very long baseline interferometry datasets that simultaneously reconstructs the full-Stokes emission structure along with the station-based gain and leakage calibration terms. DMC formulates the imaging problem in terms of posterior exploration, which is achieved using Hamiltonian Monte Carlo sampling. The resulting posterior distribution provides a natural quantification of uncertainty in both the image structure and in the data calibration. We run DMC on both synthetic and real datasets, the results of whic…
The spatial-frequency coverage of a radio interferometer is increased by combining samples acquired at different times and observing frequencies. However, astrophysical sources often contain complicated spatial structure that varies within the time-range of an observation, or the bandwidth of the receiver being used, or both. Image reconstruction algorithms can been designed to model time and frequency variability in addition to the average intensity distribution, and provide an improvement over traditional methods that ignore all variability. This paper describes an algorithm designed for suc…
We describe a new polarized imaging pipeline implemented in the FHD software package. The pipeline is based on the optimal mapmaking imaging approach and performs horizon-to-horizon image reconstruction in all polarization modes. We discuss the formalism behind the pipeline's polarized analysis, describing equivalent representations of the polarized beam response, or Jones matrix. We show that, for arrays where antennas have uniform polarization alignments, defining a non-orthogonal instrumental polarization basis enables accurate and efficient image reconstruction. Finally, we present a new c…
Next generation radio telescopes, like the Square Kilometre Array, will acquire an unprecedented amount of data for radio astronomy. The development of fast, parallelisable or distributed algorithms for handling such large-scale data sets is of prime importance. Motivated by this, we investigate herein a convex optimisation algorithmic structure, based on primal-dual forward-backward iterations, for solving the radio interferometric imaging problem. It can encompass any convex prior of interest. It allows for the distributed processing of the measured data and introduces further flexibility by…
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…
GRAVITY is the second generation Very Large Telescope Interferometer instrument for precision narrow-angle astrometry and interferometric imaging in the Near Infra-Red (NIR). It shall provide precision astrometry of order 10 microarcseconds, and imaging capability at a few milliarcsecond resolution, and hence will revolutionise dynamical measurements of celestial objects. GRAVITY is currently in the last stages of its integration and tests in Garching at MPE, and will be delivered to the VLT Interferometer (VLTI) in 2015. We present here the instrument, with a particular focus on the component…
After several generations of interferometers in radioastronomy, wide-field imaging at high angular resolution is today a major goal for trying to match optical wide-field performances. All the radio-interferometric, wide-field imaging methods currently belong to the mosaicking family. Based on a 30 years old, original idea from Ekers & Rots, we aim at proposing an alternate formalism. Starting from their ideal case, we successively evaluate the impact of the standard ingredients of interferometric imaging. A comparison with standard nonlinear mosaicking shows that both processing schemes are n…
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…
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 …
Variations of the antenna primary beam (PB) pattern as a function of time, frequency and polarization form one of the dominant direction-dependent effects at most radio frequency bands. These gains may also vary from antenna to antenna. The A-Projection algorithm, published earlier, accounts for the effects of the narrow-band antenna PB in full polarization. In this paper we present the Wide-Band A-Projection algorithm (WB A-Projection) to include the effects of wide bandwidth in the A-term itself and show that the resulting algorithm simultaneously corrects for the time, frequency and polariz…
In the context of next generation radio telescopes, like the Square Kilometre Array, the efficient processing of large-scale datasets is extremely important. Convex optimisation tasks under the compressive sensing framework have recently emerged and provide both enhanced image reconstruction quality and scalability to increasingly larger data sets. We focus herein mainly on scalability and propose two new convex optimisation algorithmic structures able to solve the convex optimisation tasks arising in radio-interferometric imaging. They rely on proximal splitting and forward-backward iteration…
Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bispectrum measurements. We reformulate this nonlin- ear problem as a linear problem for the supersymmetric rank-1 order-3 tensor formed by the tensor product of the vector representing the image under scrutiny with itself. On one hand, we propose a linear convex approach for tensor recovery with built-in supersymmetry, and regularising the inverse problem through a nuclear norm relaxation of a low-rank constraint. On the other hand, we also study a nonlinear nonconvex …
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 …
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging, leading to an alternated minimization problem. In that work, only a positivity constraint was considered, and the problem was solved by an approximated Gauss-Seidel method. In this paper, we propose to improve the approach on three fundamental aspects. Firstly, we define the estimated image as a solution of a regularized minimization problem, promoting sparsit…
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…
We conducted radio interferometric observations of six pulsars at 610 MHz using the Giant Metrewave Radio Telescope (GMRT). All these objects were claimed or suspected to be the gigahertz-peaked spectra (GPS) pulsars. For a half of the sources in our sample the interferometric imaging provides the only means to estimate their flux at 610 MHz due to a strong pulse scatter-broadening. In our case, these pulsars have very high dispersion measure values and we present their spectra containing for the first time low-frequency measurements. The remaining three pulsars were observed at low frequencie…
The desire for wide-field of view, large fractional bandwidth, high sensitivity, high spectral and temporal resolution has driven radio interferometry to the point of big data revolution where the data is represented in at least three dimensions with an axis for spectral windows, baselines, sources, etc; where each axis has its own set of sub-dimensions. The cost associated with storing and handling these data is very large, and therefore several techniques to compress interferometric data and/or speed up processing have been investigated. Unfortunately, averaging-based methods for visibility …
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 the spherical coordinate space in which they naturally live. We review these techniques, highlighting: (i) how the effectiveness of the spread spectrum phenomenon, due to the w component inducing an increase of measurement incoherence, is enhanced when going to wide fields; and (ii) how sparsity is reduced by recovering images directly on the…
The new generation of low radio-frequency interferometric arrays have enabled the imaging of the solar corona at high spectro-temporal resolutions and sensitivity. In this article we introduce and implement a formalism to generate flux density and brightness temperature ($T_{\mathrm B}$) maps from such images, using independently obtained disc-integrated solar flux density dynamic spectra. These images collectively generate a 4D data cube, with axes spanning angular coordinates ($θ,ϕ$), frequency ($ν$) and time ($t$). This 4D data cube is the most informative data product which can be generate…
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, $\mathrm{R}_{\mathrm{sing}}$, based on studying the distribution of the singular values of the measurement operator. This metho…
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…
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…
Learned Interferometric Imaging for the SPIDER Instrument
Mullard Space Science Laboratory (MSSL) University College London (UCL)（伦敦大学学院穆拉德空间科学实验室）；Department of Computer Science University College London (UCL)（伦敦大学学院计算机科学系）；Alan Turing Institute（艾伦·图灵研究所）
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…
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University College London（伦敦大学学院）；University of Geneva (UniGE)（日内瓦大学）；Lausanne University Hospital (CHUV)（洛桑大学医院）
We propose a novel regularization method for compressive imaging in the context of the compressed sensing (CS) theory with coherent and redundant dictionaries. Natural images are often complicated and several types of structures can be present at once. It is well known that piecewise smooth images exhibit gradient sparsity, and that images with extended structures are better encapsulated in wavelet frames. Therefore, we here conjecture that promoting average sparsity or compressibility over multiple frames rather than single frames is an extremely powerful regularization prior.
Data dimensionality reduction in radio interferometry can provide savings of computational resources for image reconstruction through reduced memory footprints and lighter computations per iteration, which is important for the scalability of imaging methods to the big data setting of the next-generation telescopes. This article sheds new light on dimensionality reduction from the perspective of compressed sensing theory and studies its interplay with imaging algorithms designed in the context of convex optimization. We propose a post-gridding linear data embedding to the space spanned by the l…
Multifrequency Synthesis via CHIBI: Colorful Hierarchical Interferometric Bayesian Imaging
Black Hole Initiative, Harvard University（黑洞倡议项目，哈佛大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Center for Computational Sciences, University of Tsukuba（筑波大学计算科学中心）
The brightness temperature is an effective parameter that describes the physical properties of emitting material in astrophysical objects. It is commonly determined by imaging and modeling the structure of the emitting region and estimating its flux density and angular size. Reliable approaches for visibility-based estimates of brightness temperature are needed for interferometric experiments in which poor coverage of spatial frequencies prevents successful imaging of the source structure, for example, in interferometric measurements made at millimeter wavelengths or with orbiting antennas. Su…
We describe a flagging and calibration pipeline intended for making quick look images from GMRT data. The package identifies and flags corrupted visibilities, computes calibration solutions and interpolates these onto the target source. These flagged calibrated visibilities can be directly imaged using any standard imaging package. The pipeline is written in "C" with the most compute intensive algorithms being parallelized using OpenMP.
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…
