arXiv subjects

Luke Pratley

Publications and source records attributed to Luke Pratley.

At least 19 recordsLinked to original sources

arXiv2023

Correcting Bandwidth Depolarization by Extreme Faraday Rotation

Measurements of the polarization of radio emission are subject to a number of depolarization effects such as bandwidth depolarization, which is caused by the averaging effect of a finite channel bandwidth combined with the frequency-dependent polarization caused by Faraday rotation. There have been very few mathematical treatments of bandwidth depolarization, especially in the context of the rotation measure (RM) synthesis method for analyzing radio polarization data. We have found a simple equation for predicting if bandwidth depolarization is significant for a given observational configuration. We have derived and tested three methods of modifying RM synthesis to correct for bandwidth depolarization. From these tests we have developed a new algorithm that can detect bandwidth-depolarized signals with higher signal-to-noise than conventional RM synthesis and recover the correct source polarization properties (RM and polarized intensity). We have verified that this algorithm works as expected with real data from the LOFAR Two-metre Sky Survey. To make this algorithm available to the community, we have added it as a new tool in the RM-Tools polarization analysis package.

astro-ph.IM↗

arXiv2021

Removing non-physical structure in fitted Faraday rotated signals: non-parametric QU-fitting

Next-generation spectro-polarimetric broadband surveys will probe cosmic magnetic fields in unprecedented detail, using the magneto-optical effect known as Faraday rotation. However, non-parametric methods such as RMCLEAN can introduce non-observable linearly polarized flux into a fitted model at negative wavelengths squared. This leads to Faraday rotation structures that are consistent with the observed data, but would be impossible or difficult to measure. We construct a convex non-parametric $QU$-fitting algorithm to constrain the flux at negative wavelengths squared to be zero. This allows the algorithm to recover structures that are limited in complexity to the observable region in wavelength squared. We verify this approach on simulated broadband data sets where we show that it has a lower root mean square error and that it can change the scientific conclusions for real observations. We advise using this prior in next-generation broadband surveys that aim to uncover complex Faraday depth structures. We provide a public Python implementation of the algorithm at \url{https://github.com/Luke-Pratley/Faraday-Dreams}.

astro-ph.IM↗

arXiv2021

The Global Magneto-Ionic Medium Survey (GMIMS): The brightest polarized region in the Southern sky at 75cm and its implications for Radio Loop II

Using the Global Magneto-Ionic Medium Survey (GMIMS) Low-Band South (LBS) southern sky polarization survey, covering 300 to 480 MHz at 81 arcmin resolution, we reveal the brightest region in the Southern polarized sky at these frequencies. The region, G150-50, covers nearly 20deg$^2$, near (l,b)~(150 deg,-50 deg). Using GMIMS-LBS and complementary data at higher frequencies (~0.6--30 GHz), we apply Faraday tomography and Stokes QU-fitting techniques. We find that the magnetic field associated with G150-50 is both coherent and primarily in the plane of the sky, and indications that the region is associated with Radio Loop II. The Faraday depth spectra across G150-50 are broad and contain a large-scale spatial gradient. We model the magnetic field in the region as an expanding shell, and we can reproduce both the observed Faraday rotation and the synchrotron emission in the GMIMS-LBS band. Using QU-fitting, we find that the Faraday spectra are produced by several Faraday dispersive sources along the line-of-sight. Alternatively, polarization horizon effects that we cannot model are adding complexity to the high-frequency polarized spectra. The magnetic field structure of Loop II dominates a large fraction of the sky, and studies of the large-scale polarized sky will need to account for this object. Studies of G150-50 with high angular resolution could mitigate polarization horizon effects, and clarify the nature of G150-50.

astro-ph.GA↗

arXiv2021

Sparse image reconstruction on the sphere: a general approach with uncertainty quantification

Inverse problems defined naturally on the sphere are becoming increasingly of interest. In this article we provide a general framework for evaluation of inverse problems on the sphere, with a strong emphasis on flexibility and scalability. We consider flexibility with respect to the prior selection (regularization), the problem definition - specifically the problem formulation (constrained/unconstrained) and problem setting (analysis/synthesis) - and optimization adopted to solve the problem. We discuss and quantify the trade-offs between problem formulation and setting. Crucially, we consider the Bayesian interpretation of the unconstrained problem which, combined with recent developments in probability density theory, permits rapid, statistically principled uncertainty quantification (UQ) in the spherical setting. Linearity is exploited to significantly increase the computational efficiency of such UQ techniques, which in some cases are shown to permit analytic solutions. We showcase this reconstruction framework and UQ techniques on a variety of spherical inverse problems. The code discussed throughout is provided under a GNU general public license, in both C++ and Python.

cs.IT↗

arXiv2021

Sparse Image Reconstruction for the SPIDER Optical Interferometric Telescope

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. State of the art sparse radio interferometric image reconstruction techniques have been gaining traction in radio astronomy and reconstruct accurate images of the radio sky. In this work we describe algorithms from radio interferometric imaging and sparse image reconstruction and demonstrate their application to the SPIDER concept telescope through simulated observation and reconstruction of the optical sky. Such algorithms are important for providing high fidelity images from SPIDER observations, helping to power the SPIDER concept for scientific and astronomical analysis.

astro-ph.IM↗

arXiv2020

Novel perspectives gained from new reconstruction algorithms

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 imaging over extremely wide-fields of view for the Murchison Widefield Array (MWA) telescope. Furthermore, this same mathematical framework has provided a novel understanding of wide-band polarimetry at low frequencies, where instrumental channel depolarization can be corrected through the new $δλ^2$-projection algorithm. This is a demonstration that new algorithm development outside of traditional radio astronomy is valuable for the new theoretical and practical perspectives gained. These perspectives are timely with the next generation of radio telescopes coming online.

astro-ph.IM↗

arXiv2020

Magnetism Science with the Square Kilometre Array

The Square Kilometre Array (SKA) will answer fundamental questions about the origin, evolution, properties, and influence of magnetic fields throughout the Universe. Magnetic fields can illuminate and influence phenomena as diverse as star formation, galactic dynamics, fast radio bursts, active galactic nuclei, large-scale structure, and Dark Matter annihilation. Preparations for the SKA are swiftly continuing worldwide, and the community is making tremendous observational progress in the field of cosmic magnetism using data from a powerful international suite of SKA pathfinder and precursor telescopes. In this contribution, we revisit community plans for magnetism research using the SKA, in the light of these recent rapid developments. We focus in particular on the impact that new radio telescope instrumentation is generating, thus advancing our understanding of key SKA magnetism science areas, as well as the new techniques that are required for processing and interpreting the data. We discuss these recent developments in the context of the ultimate scientific goals for the SKA era.

astro-ph.GA↗

arXiv2020

Offline and online reconstruction for radio interferometric imaging

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.

astro-ph.IM↗

arXiv2020

Wide-band Rotation Measure Synthesis

Rotation measure synthesis allows the estimation of Faraday dispersion via a Fourier transform and is the primary tool to probe cosmic magnetic fields. We show this can be considered mathematically equivalent to the one dimensional interferometric intensity measurement equation, albeit in a different Fourier space. As a result, familiar concepts in two dimensional intensity interferometry designed to correctly account for a range of instrumental conditions can be translated to the analysis of Faraday dispersion. In particular, we show how to model the effect of channel averaging during Faraday reconstruction, which has to date limited the progress of polarimetic science using wide-band measurements. Further, we simulate 1d sparse reconstruction with channel averaging for realistic frequency coverages, and show that it is possible to recover signals with large rotation measure values that were previously excluded from possible detection. This is especially important for low-frequency and wide-band polarimetry. We extended these ideas to introduce mosaicking in Faraday depth into the channel averaging process. This work, thus provides the first framework for correctly undertaking wide-band rotation measure synthesis, including the provision to add data from multiple telescopes, a prospect that should vastly improve the quality and quantity of polarimetric science. This is of particular importance for extreme environments which generate high magnetic fields such as those associated with pulsars and Fast Radio Bursts (FRBs), and will allow such sources to be accurately used as probes of cosmological fields.

astro-ph.IM↗

arXiv2019

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.

astro-ph.IM↗

arXiv2019

Load balancing for distributed interferometric image reconstruction

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 available in the PURIFY software package. Wide-field image reconstruction for data sets of this size cannot be performed effectively using the allocated computational resources without computational load balancing, demonstrating that our algorithms are critical for next-generation wide-field radio interferometers.

astro-ph.IM↗

arXiv2019

A fast and exact $w$-stacking and $w$-projection hybrid algorithm for wide-field interferometric imaging

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.

astro-ph.IM↗

arXiv2018

Approximate T-matrix and optical properties of spheroidal particles to third order in size parameter

We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical particle. T is calculated from the standard extended boundary condition method with a linear system involving two infinite matrices P and Q, whose matrix elements are integrals on the particle surface. We show that the limiting form of the P- and Q-matrices, which is different in the special case of spheroid, ensures that this Taylor expansion can be obtained by considering only multipoles of order 3 or less (i.e. dipoles, quadrupoles, and octupoles). This allows us to obtain self-contained expressions for the Taylor expansion of T(X). The lowest order is O(X^3) and equivalent to the quasi-static limit or Rayleigh approximation. Expressions to order O(X^5) are obtained by Taylor expansion of the integrals in P and Q followed by matrix inversion. We then apply a radiative correction scheme, which makes the resulting expressions valid up to order O(X^6). Orientation-averaged extinction, scattering, and absorption cross-sections are then derived. All results are compared to the exact T-matrix predictions to confirm the validity of our expressions and assess their range of applicability. For a wavelength of 400nm, the new approximation remains valid (within 1% error) up to particle dimensions of the order of 100-200nm depending on the exact parameters (aspect ratio and material). These results provide a relatively simple and computationally-friendly alternative to the standard T-matrix method for spheroidal particles smaller than the wavelength, in a size range much larger than for the commonly-used Rayleigh approximation.

physics.optics↗

arXiv2017

Online radio interferometric imaging: assimilating and discarding visibilities on arrival

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 to big-data remains difficult if not impossible in some cases. All state-of-the-art methods in RI imaging lack the ability to process data streams as they are acquired during the data observation stage. Such approaches are referred to as online processing methods. We present an online sparse regularisation methodology for RI imaging. Image reconstruction is performed simultaneously with data acquisition, where observed visibilities are assimilated into the reconstructed image as they arrive and then discarded. Since visibilities are processed online, good reconstructions are recovered much faster than standard (offline) methods which cannot start until the data acquisition stage completes. Moreover, the online method provides additional computational savings and, most importantly, dramatically reduces data storage requirements. Theoretically, the reconstructed images are of the same fidelity as those recovered by the equivalent offline approach and, in practice, very similar reconstruction fidelity is achieved. We anticipate online imaging techniques, as proposed here, will be critical in scaling RI imaging to the emerging big-data era of radio astronomy.

astro-ph.IM↗

arXiv2017

Robust sparse image reconstruction of radio interferometric observations with purify

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.

astro-ph.IM↗

arXiv2017

The w-effect in interferometric imaging: from a fast sparse measurement operator to super-resolution

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 effect increases the incoherence between the sensing basis and the sparsity basis of the signal to be recovered, leading to better estimation of the sky image. In this article, we revisit the w-projection approach using convex optimisation in realistic settings, where the measurement operator couples the w-terms in Fourier and the de-gridding kernels. We provide sparse, thus fast, models of the Fourier part of the measurement operator through adaptive sparsification procedures. Consequently, memory requirements and computational cost are significantly alleviated, at the expense of introducing errors on the radio-interferometric data model. We present a first investigation of the impact of the sparse variants of the measurement operator on the image reconstruction quality. We finally analyse the interesting super-resolution potential associated with the spread spectrum effect of the w-modulation, and showcase it through simulations. Our C++ code is available online on GitHub.

astro-ph.IM↗

arXiv2017

PURIFYing real radio interferometric observations

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 package. In particular, we implement and apply the proximal alternating direction method of multipliers (P-ADMM) algorithm presented in a recent article. We apply PURIFY to real interferometric observations. For all observations PURIFY outperforms the standard CLEAN, where in some cases PURIFY provides an improvement in dynamic range by over an order of magnitude. The latest version of PURIFY, which includes the developments presented in this work, is made publicly available.

astro-ph.IM↗

arXiv2016

ATCA observations of the MACS-Planck Radio Halo Cluster Project - I. New detection of a radio halo in PLCK G285.0-23.7

We investigate the possible presence of diffuse radio emission in the intermediate redshift, massive cluster PLCK G285.0-23.7 (z=0.39, M_500 = 8.39 x 10^(14) M_Sun). Our 16cm-band ATCA observations of PLCK G285.0-23.7 allow us to reach a rms noise level of ~11 microJy/beam on the wide-band (1.1-3.1 GHz), full-resolution (~5 arcsec) image of the cluster, making it one of the deepest ATCA images yet published. We also re-image visibilities at lower resolution in order to achieve a better sensitivity to low-surface-brightness extended radio sources. We detect one of the lowest luminosity radio halos known at z>0.35, characterised by a slight offset from the well-studied 1.4 GHz radio power vs. cluster mass correlation. Similarly to most known radio-loud clusters (i.e. those hosting diffuse non-thermal sources), PLCK G285.0-23.7 has a disturbed dynamical state. Our analysis reveals a similarly elongated X-ray and radio morphology. While the size of the radio halo in PLCK G285.0-23.7 is smaller than lower redshift radio-loud clusters in the same mass range, it shows a similar correlation with the cluster virial radius, as expected in the framework of hierarchical structure formation.

astro-ph.CO↗