http://arxiv.org/abs/1807.09239
The standard wide-field imaging technique, the $w$-projection, allows correction for wide-fields of view for non-coplanar radio interferometric arrays. However, calculating exact corrections for each measurement has not been possible due to the amount of computation required at high resolution and with the large number of visibilities from current interferometers. The required accuracy and computational cost of these corrections is one of the largest unsolved challenges facing next generation radio interferometers such as the Square Kilometre Array. We show that the same calculation can be performed with a radially symmetric $w$-projection kernel, where we use one dimensional adaptive quadrature to calculate the resulting Hankel transform, decreasing the computation required for kernel generation by several orders of magnitude, whilst preserving the accuracy. We demonstrate the potential of our radially symmetric $w$-projection kernel via sparse image reconstruction, using the software package Purify. We develop an MPI distributed $w$-stacking and $w$-projection hybrid algorithm, where we apply exact $w$-term corrections for 100 million measurements with $w$-terms between $\pm 300$ wavelengths, for a $17^\circ$ field of view and image size of 4096 by 4096 pixels. The pre-computation and reconstruction took a total time of 35 minutes. Such a level of accuracy and scalability is not possible with standard $w$-projection kernel generation methods. This demonstrates that we can scale to the large number of measurements and large image sizes expected from next generation interferometers whilst still maintaining both speed and accuracy. This work is a critical development for resolving one of the biggest unsolved challenges in interferometry.
L. Pratley, M. Johnston-Hollitt and J. McEwen
Wed, 25 Jul 18
11/60
Comments: 6 Figures, 19 Pages. Submitted to ApJ
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