Advances in Calibration and Imaging Techniques in Radio Interferometry

This paper summarizes some of the major calibration and image reconstruction techniques used in radio interferometry and describes them in a common mathematical framework. The use of this framework has a number of benefits, ranging from clarification of the fundamentals, use of standard numerical optimization techniques, and generalization or specialization to new algorithms

Distributed image reconstruction for very large arrays in radio astronomy

Current and future radio interferometric arrays such as LOFAR and SKA are characterized by a paradox. Their large number of receptors (up to millions) allow theoretically unprecedented high imaging resolution. In the same time, the ultra massive amounts of samples makes the data transfer and computational loads (correlation and calibration) order of magnitudes too high to allow any currently existing image reconstruction algorithm to achieve, or even approach, the theoretical resolution. We investigate here decentralized and distributed image reconstruction strategies which select, transfer and process only a fraction of the total data. The loss in MSE incurred by the proposed approach is evaluated theoretically and numerically on simple test cases.Comment: Sensor Array and Multichannel Signal Processing Workshop (SAM), 2014 IEEE 8th, Jun 2014, Coruna, Spain. 201

Direction-Dependent Polarised Primary Beams in Wide-Field Synthesis Imaging

The process of wide-field synthesis imaging is explored, with the aim of understanding the implications of variable, polarised primary beams for forthcoming Epoch of Reionisation experiments. These experiments seek to detect weak signatures from redshifted 21cm emission in deep residual datasets, after suppression and subtraction of foreground emission. Many subtraction algorithms benefit from low side-lobes and polarisation leakage at the outset, and both of these are intimately linked to how the polarised primary beams are handled. Building on previous contributions from a number of authors, in which direction-dependent corrections are incorporated into visibility gridding kernels, we consider the special characteristics of arrays of fixed dipole antennas operating around 100-200 MHz, looking towards instruments such as the Square Kilometre Array (SKA) and the Hydrogen Epoch of Reionization Arrays (HERA). We show that integrating snapshots in the image domain can help to produce compact gridding kernels, and also reduce the need to make complicated polarised leakage corrections during gridding. We also investigate an alternative form for the gridding kernel that can suppress variations in the direction-dependent weighting of gridded visibilities by 10s of dB, while maintaining compact support.Comment: 15 pages, 4 figures. Accepted for publication in JA

Blind Sensor Calibration using Approximate Message Passing

The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying them on real data can be problematic if imperfect sensing devices introduce deviations from this ideal signal ac- quisition process, caused by sensor decalibration or failure. We propose a message passing algorithm called calibration approximate message passing (Cal-AMP) that can treat a variety of such sensor-induced imperfections. In addition to deriving the general form of the algorithm, we numerically investigate two particular settings. In the first, a fraction of the sensors is faulty, giving readings unrelated to the signal. In the second, sensors are decalibrated and each one introduces a different multiplicative gain to the measures. Cal-AMP shares the scalability of approximate message passing, allowing to treat big sized instances of these problems, and ex- perimentally exhibits a phase transition between domains of success and failure.Comment: 27 pages, 9 figure

A scalable algorithm for radio-interferometric imaging

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 paper, we propose a scalable algorithm for RI imaging that offers a highly parallelizable structure paving the way for next- generation high-dimensional data imaging. The proposed algorithm is based on a proximal linear version of the alternating direction method of multipliers (ADMM)

Image formation in synthetic aperture radio telescopes

Next generation radio telescopes will be much larger, more sensitive, have much larger observation bandwidth and will be capable of pointing multiple beams simultaneously. Obtaining the sensitivity, resolution and dynamic range supported by the receivers requires the development of new signal processing techniques for array and atmospheric calibration as well as new imaging techniques that are both more accurate and computationally efficient since data volumes will be much larger. This paper provides a tutorial overview of existing image formation techniques and outlines some of the future directions needed for information extraction from future radio telescopes. We describe the imaging process from measurement equation until deconvolution, both as a Fourier inversion problem and as an array processing estimation problem. The latter formulation enables the development of more advanced techniques based on state of the art array processing. We demonstrate the techniques on simulated and measured radio telescope data.Comment: 12 page

Radio Astronomical Image Formation using Constrained Least Squares and Krylov Subspaces

Image formation for radio astronomy can be defined as estimating the spatial power distribution of celestial sources over the sky, given an array of antennas. One of the challenges with image formation is that the problem becomes ill-posed as the number of pixels becomes large. The introduction of constraints that incorporate a-priori knowledge is crucial. In this paper we show that in addition to non-negativity, the magnitude of each pixel in an image is also bounded from above. Indeed, the classical "dirty image" is an upper bound, but a much tighter upper bound can be formed from the data using array processing techniques. This formulates image formation as a least squares optimization problem with inequality constraints. We propose to solve this constrained least squares problem using active set techniques, and the steps needed to implement it are described. It is shown that the least squares part of the problem can be efficiently implemented with Krylov subspace based techniques, where the structure of the problem allows massive parallelism and reduced storage needs. The performance of the algorithm is evaluated using simulations