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. @en

Current and future radio telescopes deal with large volumes of data and are expected to generate high resolution gigapixel-size images. The imaging problem in radio interferometry is highly ill-posed and the choice of prior model of the sky is of utmost importance to guarantee a reliable reconstruction. Traditionally, one or more regularization terms (e.g. sparsity and positivity) are applied for the complete image. However, radio sky images can often contain individual source facets in a large empty background. More precisely, we propose to divide radio images into source occupancy regions (facets) and apply relevant regularizing assumptions for each facet. Leveraging a stochastic primal dual algorithm, we show the potential merits of applying facet-based regularization on the radio-interferometric images which results in both computation time and memory requirement savings.

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We propose a fast iterative method for image formation in Radio Astronomy (RA). We formulate the image formation problem as a maximum likelihood estimation problem to estimate the image pixel powers via array covariance measurements. We use an iterative solution method based on projections onto Krylov subspaces and exploit the sample covariance error estimate via discrepancy principle as the stopping criterion. We propose to regularize the ill-posed imaging problem based on a Bayesian framework using MVDR beamformed data applied as a right preconditioner to the system matrix. We compare the proposed method with the state-of-the-art sparse sensing methods and show that the proposed method obtains comparably accurate solutions with a significant reduction in computation.

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Image formation in radio astronomy is a large-scale inverse problem that is inherently illposed. We present a general algorithmic framework based on a Bayesian-inspired regularized maximum likelihood formulation of the radio astronomical imaging problem with a focus on diffuse emission recovery from limited noisy correlation data. The algorithm is dubbed PRIor-conditioned Fast Iterative Radio Astronomy and is based on a direct embodiment of the regularization operator into the system by right preconditioning. The resulting system is then solved using an iterative method based on projections onto Krylov subspaces. We motivate the use of a beam-formed image (which includes the classical 'dirty image') as an efficient prior-conditioner. Iterative reweighting schemes generalize the algorithmic framework and can account for different regularization operators that encourage sparsity of the solution. The performance of the proposed method is evaluated based on simulated 1D and 2D array arrangements as well as actual data from the core stations of the Low Frequency Array radio telescope antenna configuration, and compared to state-of-the-art imaging techniques. We show the generality of the proposed method in terms of regularization schemes while maintaining a competitive reconstruction quality with the current reconstruction techniques. Furthermore, we show that exploiting Krylov subspace methods together with the proper noise-based stopping criteria results in a great improvement in imaging efficiency.

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A fast iterative method based on projection onto Krylov subspaces has been proposed for Radio Astronomical (RA) image reconstruction from telescope array measurements. The image formation problem is formulated as a linear least squares (LS) estimation problem by discretizing the Field of View (FoV) of the telescope array into a number of pixels. The ill-posed imaging problem is regularized by the Krylov iterations and the system matrix is prior conditioned by the weights attained from the matched filter beamformed data. The performance of the proposed method is shown based on simulated data from a single station of the the Low Frequency Array Radio Telescope (LOFAR) antenna configuration on a test radio astronomical image. It has been shown that the prior conditioning of the system matrix results in a more accurate image estimate by reducing the artifacts introduced in the empty parts of the image. Furthermore, it was shown that Krylov-based methods fit very well in the context of large scale RA image reconstruction due to their speed and computational benefits.@en

A simple and novel algorithm for source recovery based on array data measurements in radio astronomy is proposed. Considering that a radioastronomical image is composed of both point sources and extended emissions, prior information on the images, namely non-negativity and substantial black background are taken into account to choose source representation basis functions. Dirac delta functions are chosen to represent point sources and a Gaussian function approximated from the main beam of the antenna array is selected to capture the extended emissions. We apply the non-negative least squares (NNLS) algorithm to estimate the basis coefficients. It is shown that the sparsity promoted by the NNLS algorithm based on the chosen basis functions results in a super-resolution (finer resolution than prescribed by the main beam of the antenna array pattern) estimate for the point sources and smooth recovery for the extended emissions.@en

Image formation using the data from an array of sensors is a familiar problem in many fields such as radio astronomy, biomedical and geodetic imaging. The problem can be formulated as a least squares (LS) estimation problem and becomes ill-posed at high resolutions, i.e. large number of image pixels. In this paper we propose two regularization methods, one based on weighted truncation of the eigenvalue decomposition of the image deconvolution matrix and the other based on the prior knowledge of the "dirty image" using the available data. The methods are evaluated by simulations as well as actual data from a phased-array radio telescope in the Netherlands, the Low Frequency Array Radio Telescope (LOFAR).@en

Providing automated granular control of lighting, along with user-driven control, results in an energy-efficient smart lighting system design while catering to personal occupant preferences. Two functional ingredients in such a system are: 1) sensing that provides granular information on occupant location and 2) a communication system to transmit control messages from a user. In this paper, we consider an ultrasonic circular array sensor that provides the dual functionality of granular occupant sensing and a communication receiver for user control transmissions. A ceiling-mounted sensor configuration with a colocated ultrasonic transmitter and array receiver is considered. To perform presence sensing, this transmitter sends periodic bursts of sinusoidal pulses that, upon reflection from the environment, are received at the array sensor. The echoes are processed to obtain estimates of range, azimuth, and elevation angles corresponding to possible occupant movements. A Kalman filter based on a near constant velocity model is used for target tracking. The resulting occupant location is used for energy-efficient lighting control. A user may in addition control lamps in its vicinity by sending messages at ultrasonic frequency, which are processed by the receiver array, and used to further adapt requested parameters of the lighting system. The proposed sensing and messaging solution is tested in an indoor office space with an eight-element receiver array sensor prototype.@en