Image formation for future radio telescopes

Fundamental scientific questions such as how the first stars were formed or how the universe came into existence and evolved to its present state drive us to observe weak radio signals impinging on the earth from the early days of the universe. During the last century, radio astronomy has been vastly advancing. Important discoveries on the formation of various celestial objects such as pulsars, neutron stars, black holes, radio galaxies and quasars are the result of radio astronomical observations. To study celestial objects and the astrophysical processes that are responsible for their radio emissions, images must be formed. This is done with the help of large radio telescope arrays. Next generation radio telescopes such as the Low Frequency Array Radio Telescope (LOFAR) [1] and the Square Kilometer Array (SKA) [2], bring about increasingly more observational evidence for the study of the radio sky by generating very high resolution and high fidelity images. In this dissertation, we study radio astronomical imaging as the problem of estimating the sky spatial intensity distribution over the field of view of the radio telescope array from the incomplete and noisy array data. The increased sensitivity, resolution and sky coverage of the new instruments pose additional challenges to the current radio astronomical imaging pipeline. Namely, the large amount of data captured by the radio telescopes cannot be stored and needs to be processed quasi-real time. Many pixel-based imaging algorithms, such as the widely-used CLEAN [3] algorithm, are not scalable to the size of the required images and perform very slow in high resolution scenarios. Therefore, there is an urgent need for new efficient imaging algorithms. Moreover, regardless of the amount of collected data, there is an inherent loss of information in the measurement process due to physical limitations. Therefore, to recover physically meaningful images additional information in the form of constraints and regularizing assumptions are necessary. The central objective of the current dissertation is to introduce advanced algebraic techniques together with custom-made regularization schemes to speed up the image formation pipeline of the next generation radio telescopes.Circuits and System