Abstract
Radio interferometers do not measure the sky brightness distribution directly, but measure a modified Fourier transform of it. Imaging algorithms therefore need a computational representation of the linear measurement operator and its adjoint, regardless of the specific chosen imaging algorithm. In this paper, we present a C++ implementation of the radio interferometric measurement operator for wide-field measurements that is based on so-called improved w-stacking. It can provide high accuracy (down to ≈10−12), is based on a new gridding kernel that allows smaller kernel support for given accuracy, dynamically chooses kernel, kernel support, and oversampling factor for maximum performance, uses piece-wise polynomial approximation for cheap evaluations of the gridding kernel, treats the visibilities in cache-friendly order, uses explicit vectorisation if available, and comes with a parallelisation scheme that scales well also in the adjoint direction (which is a problem for many previous implementations). The implementation has a small memory footprint in the sense that temporary internal data structures are much smaller than the respective input and output data, allowing in-memory processing of data sets that needed to be read from disk or distributed across several compute nodes before.
Highlights
The central data analysis task in radio interferometry derives the location-dependent sky brightness distribution I(l, m) from a set of complex-valued measured visibilities dk
It can provide high accuracy, is based on a new gridding kernel that allows smaller kernel support for given accuracy, dynamically chooses kernel, kernel support, and oversampling factor for maximum performance, uses piece-wise polynomial approximation for cheap evaluations of the gridding kernel, treats the visibilities in cache-friendly order, uses explicit vectorisation if available, and comes with a parallelisation scheme that scales well in the adjoint direction
While taking the noise into account is the task of the chosen imaging algorithm, all such algorithms need an implementation of Eq (1)
Summary
The central data analysis task in radio interferometry derives the location-dependent sky brightness distribution I(l, m) from a set of complex-valued measured visibilities dk. Increasing the oversampling factor allows a reduction of the convolution kernel support size while keeping the overall accuracy constant, which reduces the time required for the actual gridding or degridding step.
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