Adaptive Weighting in Radio Interferometric Imaging

Radio interferometers observe the Fourier space of the sky, at locations determined by the array geometry. Before a real space image is constructed by a Fourier transform, the data is weighted to improve the quality of reconstruction. Two criteria for calculation of weights are maximizing sensitivity and minimizing point spread function (PSF) sidelobe levels. In this paper, we propose a novel weighting scheme suitable for ultra deep imaging experiments. The proposed weighting scheme is used to maximize sensitivity while minimizing PSF sidelobe variation across frequency and multiple epochs. We give simulation results that show the superiority of the proposed scheme compared with commonly used weighting schemes in achieving these objectives.Comment: MNRAS Accepted 2014 July 22. Received 2014 July 15; in original form 2014 June 2

Radio Interferometric Calibration Using a Riemannian Manifold

In order to cope with the increased data volumes generated by modern radio interferometers such as LOFAR (Low Frequency Array) or SKA (Square Kilometre Array), fast and efficient calibration algorithms are essential. Traditional radio interferometric calibration is performed using nonlinear optimization techniques such as the Levenberg-Marquardt algorithm in Euclidean space. In this paper, we reformulate radio interferometric calibration as a nonlinear optimization problem on a Riemannian manifold. The reformulated calibration problem is solved using the Riemannian trust-region method. We show that calibration on a Riemannian manifold has faster convergence with reduced computational cost compared to conventional calibration in Euclidean space.Comment: Draft version. Final version will appear in IEEE ICASSP 2013, http://www.icassp2013.com

Fundamental Limitations of Pixel Based Image Deconvolution in Radio Astronomy

Deconvolution is essential for radio interferometric imaging to produce scientific quality data because of finite sampling in the Fourier plane. Most deconvolution algorithms are based on CLEAN which uses a grid of image pixels, or clean components. A critical matter in this process is the selection of pixel size for optimal results in deconvolution. As a rule of thumb, the pixel size is chosen smaller than the resolution dictated by the interferometer. For images consisting of unresolved (or point like) sources, this approach yields optimal results. However, for sources that are not point like, in particular for partially resolved sources, the selection of right pixel size is still an open issue. In this paper, we investigate the limitations of pixelization in deconvolving extended sources. In particular, we pursue the usage of orthonormal basis functions to model extended sources yielding better results than by using clean components.Comment: 4 pages, 5 figures, the 6th IEEE Sensor Array and Multichannel Signal Processing worksho

Robust Radio Interferometric Calibration Using the t-Distribution

A major stage of radio interferometric data processing is calibration or the estimation of systematic errors in the data and the correction for such errors. A stochastic error (noise) model is assumed, and in most cases, this underlying model is assumed to be Gaussian. However, outliers in the data due to interference or due to errors in the sky model would have adverse effects on processing based on a Gaussian noise model. Most of the shortcomings of calibration such as the loss in flux or coherence, and the appearance of spurious sources, could be attributed to the deviations of the underlying noise model. In this paper, we propose to improve the robustness of calibration by using a noise model based on Student's t distribution. Student's t noise is a special case of Gaussian noise when the variance is unknown. Unlike Gaussian noise model based calibration, traditional least squares minimization would not directly extend to a case when we have a Student's t noise model. Therefore, we use a variant of the Expectation Maximization (EM) algorithm, called the Expectation-Conditional Maximization Either (ECME) algorithm when we have a Student's t noise model and use the Levenberg-Marquardt algorithm in the maximization step. We give simulation results to show the robustness of the proposed calibration method as opposed to traditional Gaussian noise model based calibration, especially in preserving the flux of weaker sources that are not included in the calibration model.Comment: MNRAS accepte

Reduced Ambiguity Calibration for LOFAR

Interferometric calibration always yields non unique solutions. It is therefore essential to remove these ambiguities before the solutions could be used in any further modeling of the sky, the instrument or propagation effects such as the ionosphere. We present a method for LOFAR calibration which does not yield a unitary ambiguity, especially under ionospheric distortions. We also present exact ambiguities we get in our solutions, in closed form. Casting this as an optimization problem, we also present conditions for this approach to work. The proposed method enables us to use the solutions obtained via calibration for further modeling of instrumental and propagation effects. We provide extensive simulation results on the performance of our method. Moreover, we also give cases where due to degeneracy, this method fails to perform as expected and in such cases, we suggest exploiting diversity in time, space and frequency.Comment: Draft version. Final version published on 10 April 201