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 sparsity prior in the context of a reweighted analysis approach (SARA). The resulting approach is dubbed Polarized SARA. We demonstrate on simulated observations of M87 with the Event Horizon Telescope that imposing the polarization constraint leads to superior image quality. The results also confirm that the performance of the average sparsity prior surpasses the alternative state-of-the-art priors for polarimetric imaging.
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…
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…
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…
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…
Residual calibration errors are difficult to predict in interferometric radio polarimetry because they depend on the employed observational calibration strategy, encompassing the Stokes vector of the calibrator and parallactic angle coverage. This work presents analytic derivations and simulations that enable examination of residual on-axis instrumental leakage and position angle errors for a suite of calibration strategies. The focus is on arrays comprising alt-az antennas with common feeds over which parallactic angle is approximately uniform. The results indicate that calibration schemes re…
New generation of radio interferometers are envisaged to produce high quality, high dynamic range Stokes images of the observed sky from the corresponding under-sampled Fourier domain measurements. In practice, these measurements are contaminated by the instrumental and atmospheric effects that are well represented by Jones matrices, and are most often varying with observation direction and time. These effects, usually unknown, act as a limiting factor in achieving the required imaging performance and thus, their calibration is crucial. To address this issue, we develop a global algorithm, nam…
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…
Next generation radio telescope arrays are being designed and commissioned to accurately measure polarized intensity and rotation measures across the entire sky through deep, wide-field radio interferometric surveys. Radio interferometer dish antenna arrays are affected by direction-dependent (DD) gains due to both instrumental and atmospheric effects. In this paper we demonstrate the effect of DD errors for parabolic dish antenna array on the measured polarized intensities of radio sources in interferometric images. We characterize the extent of polarimetric image degradation due to the DD ga…
In a companion paper, we presented BayesCal, a mathematical formalism for mitigating sky-model incompleteness in interferometric calibration. In this paper, we demonstrate the use of BayesCal to calibrate the degenerate gain parameters of full-Stokes simulated observations with a HERA-like hexagonal close-packed redundant array, for three assumed levels of completeness of the a priori known component of the calibration sky model. We compare the BayesCal calibration solutions to those recovered by calibrating the degenerate gain parameters with only the a priori known component of the calibrati…
The Murchison Wide-field Array (MWA) is a low frequency radio telescope, currently under construction, intended to search for the spectral signature of the epoch of re-ionisation (EOR) and to probe the structure of the solar corona. Sited in Western Australia, the full MWA will comprise 8192 dipoles grouped into 512 tiles, and be capable of imaging the sky south of 40 degree declination, from 80 MHz to 300 MHz with an instantaneous field of view that is tens of degrees wide and a resolution of a few arcminutes. A 32-station prototype of the MWA has been recently commissioned and a set of obser…
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…
Current-generation low frequency interferometers constructed with the objective of detecting the high-redshift 21 cm background, aim to generate power spectra of the brightness-temperature contrast of neutral hydrogen in primordial intergalactic medium. Two-dimensional power spectra (power in Fourier modes parallel and perpendicular to the line of sight) formed from interferometric visibilities have been shown to delineate a boundary between spectrally-smooth foregrounds (known as the wedge) and spectrally-structured 21 cm background emission (the EoR-window). However, polarized foregrounds ar…
Linearly polarized emission is described, in general, in terms of the Stokes parameters $Q$ and $U$, from which the polarization intensity and polarization angle can be determined. Although the polarization intensity and polarization angle provide an intuitive description of the polarization, they are affected by the limitations of interferometric data, such as missing single-dish data in the u-v plane, from which radio frequency interferometric data is visualized. To negate the effects of these artefacts, it is desirable for polarization diagnostics to be rotationally and translationally inva…
Coronal magnetic fields are well known to be one of the crucial parameters defining coronal physics and space weather. However, measuring the global coronal magnetic fields remains challenging. The polarization properties of coronal radio emissions are sensitive to coronal magnetic fields. While they can prove to be useful probes of coronal and heliospheric magnetic fields, their usage has been limited by technical and algorithmic challenges. We present a robust algorithm for precise polarization calibration and imaging of low-radio frequency solar observations and demonstrate it on data from …
