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 performed with a radially symmetric $w$-projection kernel, where we use one dimensional adaptive quadrature to calculate the resulting Hankel transform, decreasing the computation required for kernel generation by several orders of magnitude, whilst preserving the accuracy. We confirm that the radial $w$-projection kernel is accurate to approximately 1% by imaging the zero-spacing with an added $w$-term. We demonstrate the potential of our radially symmetric $w$-projection kernel via sparse image reconstruction, using the software package PURIFY. We develop a distributed $w$-stacking and $w$-projection hybrid algorithm. We apply this algorithm to individually correct for non-coplanar effects in 17.5 million visibilities over a $25$ by $25$ degree field of view MWA observation for image reconstruction. Such a level of accuracy and scalability is not possible with standard $w$-projection kernel generation methods. This demonstrates that we can scale to a large number of measurements with large image sizes whilst still maintaining both speed and accuracy.
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…
We present a new algorithm for stacking radio interferometric data in the uv-domain. The performance of uv-stacking is compared to the stacking of fully imaged data using simulated Atacama Large Millimeter/sub-millimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA) deep extragalactic surveys. We find that image- and uv-stacking produce similar results, however, uv-stacking is typically the more robust method. An advantage of the uv-stacking algorithm is the availability of uv-data post stacking, which makes it possible to identify and remove problematic baselines. For deep VLA su…
The ViSta method for optimized stacking of broadband interferometric data in the Fourier domain
Scuola Internazionale Superiore di Studi Avanzati（高等师范学校）；INAF - Istituto di Radioastronomia - Italian ALMA Regional Centre（国家天体物理研究所射电天文台意大利ALMA区域中心）；Institute for Fundamental Physics of the Universe (IFPU)（宇宙基础物理研究所）；INAF - Istituto di Radioastronomia（国家天体物理研究所射电天文台）；Istituto Nazionale Fisica Nucleare (INFN), Sezione di Trieste（国家核物理研究所的里雅斯特分部）
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…
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…
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…
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 …
Stacking as a tool for studying objects that are not individually detected is becoming popular even for radio interferometric data, and will be widely used in the SKA era. Stacking is typically done using imaged data rather than directly using the visibilities (the uv-data). We have investigated and developed a novel algorithm to do stacking using the uv-data. We have performed exten- sive simulations comparing to image-stacking, and summarize the results of these simulations. Furthermore, we disuss the implications in light of the vast data volume produced by the SKA. Having access to the uv-…
W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the a…
We analyse the accuracy of radio interferometric gridding of visibilities with the aim to quantify the Epoch of Reionization (EoR) 21-cm power spectrum bias caused by gridding, ultimately to determine the suitability of different imaging algorithms and gridding settings for 21-cm power spectrum analysis. We simulate realistic LOFAR data, and construct power spectra with convolutional gridding and w-stacking, w-projection, image domain gridding and without w-correction. These are compared against directly Fourier transformed data. The influence of oversampling, kernel size, w-quantization, kern…
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…
Astronomical widefield imaging of interferometric radio data is computationally expensive, especially for the large data volumes created by modern non-coplanar many-element arrays. We present a new widefield interferometric imager that uses the w-stacking algorithm and can make use of the w-snapshot algorithm. The performance dependencies of CASA's w-projection and our new imager are analysed and analytical functions are derived that describe the required computing cost for both imagers. On data from the Murchison Widefield Array, we find our new method to be an order of magnitude faster than …
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 t…
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…
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…
Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry where knowledge of the illumination pattern beyond the native spatial resolution of the image may be required. Here, we introduce a method of PSF reconstruction where point sources are artificially sampled beyond the native resolution of an image and combined together via stacking to return a finely sampled estimate of the PSF. This estimate is then deconvolved…
Wide-field radio interferometric telescopes such as the Square Kilometre Array now being designed are subject to a number of aberrations. One particularly pernicious aberration is that due to non-coplanar baselines whereby long baselines incur a quadratic image-plane phase error. There are numerous algorithms for dealing with the non-coplanar baselines effect. As a result of our experience with developing processing software for the Australian Square Kilometre Array Pathfinder, we advocate the use of a hybrid algorithm, called w snapshots, based on a combination of w projection and snapshot im…
The effects of the antenna far-field power pattern limits the imaging performance of modern wide-bandwidth, high-sensitivity interferometric radio telescopes. Given a model for the aperture illumination pattern (AIP) of the antenna, referred to as the A-term, the wide-band (WB) A-Projection algorithm corrects for the effects of its time, frequency, and polarization structure. The level to which this correction is possible depends on how accurately the A-term, represents the true AIP. In this paper, we describe the A-Solver methodology that combines physical modeling with optimization to hologr…
Radio interferometers do not measure the sky brightness distribution directly but rather a modified Fourier transform of it. Imaging algorithms, thus, need a computational representation of the linear measurement operator and its adjoint, irrespective of the specific chosen imaging algorithm. In this paper, we present a C++ implementation of the radio interferometric measurement operator for wide-field measurements which is based on "improved $w$-stacking". It can provide high accuracy (down to $\approx 10^{-12}$), is based on a new gridding kernel which allows smaller kernel support for given…
A radio interferometer indirectly measures the intensity distribution of the sky over the celestial sphere. Since measurements are made over an irregularly sampled Fourier plane, synthesising an intensity image from interferometric measurements requires substantial processing. Furthermore there are distortions that have to be corrected. In this thesis, a new high-performance image synthesis tool (imaging tool) for radio interferometry is developed. Implemented in C++ and CUDA, the imaging tool achieves unprecedented performance by means of Graphics Processing Units (GPUs). The imaging tool is …
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 …
Since the 1970s, much of traditional interferometric imaging has been built around variations of the CLEAN algorithm, in both terminology, methodology, and algorithm development. Recent developments in applying new algorithms from convex optimization to interferometry has allowed old concepts to be viewed from a new perspective, ranging from image restoration to the development of computationally distributed algorithms. We present how this has ultimately led the authors to new perspectives in wide-field imaging, allowing for the first full individual non-coplanar corrections applied during ima…
(abridged) The Atacama Large Aperture Submillimeter Telescope (AtLAST) project aims to build a 50-m-class submm telescope with $>1^\circ$ field of view, high in the Atacama Desert, providing fast and detailed mapping of the mm/submm sky. It will thus serve as a strong complement to existing facilities such as ALMA. ALMA's small field of view ($<15^{\prime\prime}$ at 350 GHz) limits its mapping speed for large surveys. Instead, a single dish with a large field of view such as the AtLAST concept can host large multi-element instruments that can more efficiently map large portions of the sky. Sma…
