Accurate image reconstruction in radio interferometry
This thesis is concerned with accurate imaging from radio interferometry data and with subsequent analysis so as to determine source positions and fluxes in the radio sky. The thesis makes proposals and implementations of new algorithms, which substantially improve the accuracy of image products and the results of source extraction. These improvements in accuracy promise to assist scientific research into astronomical objects and phenomena in radio astronomy. The thesis contains six chapters, beginning with an overview of the imaging process in radio interferometry in Chapter 1. Chapter 2 focuses on improving the accuracy of source extraction, by utilising the Bayesian methodology. The proposed Bayesian method has been implemented in a software package called 'BaSC' which uses the Markov Chain Monte Carlo (MCMC) technique. By design, it works with intermediate radio interferometry image products, such as dirty images, rather than with reconstructed images. BaSC achieves greater precision in source location and better resolving power than mainstream source extraction software such as SExtractor, which works with reconstructed images. This finding confirms that reconstructed images are not a true representation of the radio sky, whereas dirty images already contain full information about the observations. This piece of work has been accepted by Monthly Notices of the Royal Astronomical Society (Hague et al. 2018). Chapter 2 is based on this paper, but has been rewritten and expanded. Based on this conclusion, Chapter 3 seeks to optimise the gridding process so as to make accurate dirty images. Since the Fast Fourier transform (FFT) produces dirty images with a much lower computational cost than the Direct Fourier transform (DFT), a new gridding function is needed which minimises the difference between DFT and FFT dirty images. The 'Least-misfit' gridding function is proposed, so as to minimise the image misfit between the DFT and FFT dirty images, and this is implemented and tested. Given an identical support width, it outperforms the main-stream spheroidal function in the image misfit by a factor of at least 100, it also suppresses aliasing in the image plane better. Aliasing is essentially a part of the image misfit, so there is no need to consider it separately. The least-misfit gridding function, with a support width of 7 and an image cropping rate of 0.5, is recommended for application to both the gridding and degridding processes, and makes it realistic to achieve the limit of single precision arithmetic in the image misfit and visibility misfit. With the new gridding function in place, Chapter 4 proposes two novel wide-field imaging algorithms: improved W-Stacking and N-Faceting. The improved W-Stacking method uses a three-dimensional gridding, rather than two-dimensional gridding as in the original W-Stacking method. This renders possible the calculation and application of the correcting function on the $n$ (third) dimension. This improvement greatly increases the accuracy of the FFT dirty image on the celestial sphere, relative to the DFT dirty image. The image misfit is as small as $10^{-8}$ when using the proposed least-misfit gridding function with a support width of 8, and it further reaches the double precision limit when the support width is increased to 14. For comparison, the image misfit levels achieved by the W-Projection algorithm in CASA and the original W-Stacking algorithm in WSCLEAN are $10^{-3}$, several orders of magnitude worse. In addition, since the number of $w$-planes required by the improved W-Stacking method is reduced compared to the original method, cutting a significant amount of FFT computational cost. As for the original W-Stacking method, if less $w$-planes than needed are used, the dirty images and reconstructed images produced will underestimate the fluxes of sources that are located far from the phase centre. The N-Faceting method involves imaging of multiple $n$-planes, followed by a three-dimensional deconvolution process, where a position-independent beam is used. Chapter 5 applies the improved W-Stacking method to two real sets of observational data, comprising one GMRT dataset and one VLA dataset. The dirty images on the celestial sphere and the reconstructed images are shown. The improved W-Stacking method successfully removes non-coplanar effects. For the observation with a larger range of $w$, improved W-Stacking method is recommended to generate a more accurate image with lower computational cost compared to the original W-Stacking method. Finally, Chapter 6 sets out conclusions drawn from the present work.
radio interferometry, image processing, gridding, degridding, MCMC, Astronomical source extraction, N-Faceting method, wide field imaging, high accuracy imaging, Clustering
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