Using baseline-dependent window functions for data compression and field-of-interest shaping in radio interferometry

Abstract

In radio interferometry, observed visibilities are intrinsically sampled at some interval in time and frequency. Modern interferometers are capable of producing data at very high time and frequency resolution; practical limits on storage and computation costs require that some form of data compression be imposed. The traditional form of compression is a simple averaging of the visibilities over coarser time and frequency bins. This has an undesired side effect: the resulting averaged visibilities "decorrelate", and do so differently depending on the baseline length and averaging interval. This translates into a non-trivial signature in the image domain known as "smearing", which manifests itself as an attenuation in amplitude towards off-centre sources. With the increasing fields of view and/or longer baselines employed in modern and future instruments, the trade-off between data rate and smearing becomes increasingly unfavourable. In this work we investigate alternative approaches to lowloss data compression. We show that averaging of the visibility data can be treated as a form of convolution by a boxcar-like window function, and that by employing alternative baseline-dependent window functions a more optimal interferometer smearing response may be induced. In particular, we show improved amplitude response over a chosen field of interest, and better attenuation of sources outside the field of interest. The main cost of this technique is a reduction in nominal sensitivity; we investigate the smearing vs. sensitivity trade-off, and show that in certain regimes a favourable compromise can be achieved. We show the application of this technique to simulated data from the Karl G. Jansky Very Large Array (VLA) and the European Very-longbaseline interferometry Network (EVN).

Baseline-dependent sampling and windowing for radio interferometry: data compression, field-of-interest shaping, and outer field suppression

“…[uv] pqkr are normalised boxcar window functions defined in tν-space and uv-space respectively. The detailed derivations for these equations are developed in Atemkeng et al (2016). Eq.…”

“…(38) and (39) are of critical importance on the squared error norm in each pixel of the dirty image and so they merit detailed explanation: 1) In tν-space, the length of the window X(u, v) (BDWF) remains constant across all baselines while the window resolution varies on different baselines: in this sense, X(u, v) is baseline-dependent. Because the length of X(u, v) is constant along all the baselines, the compression factor also remains constant across all the baselines, as when applying a simple averaging (see Atemkeng et al (2016)). 2) In tν-space, the window XBDA(u, v) (BDAWF) varies in length (hence the extrat index BDA) and resolution across all baselines.…”

“…Results show that decorrelation/smearing is severe on longer East-West baselines than shorter East-West baselines and that smearing is a function of source position in the sky. Simple averaging could be used in a way to increase the signal-to-noise ratio (SNR) within the FoI by suppressing the sidelobes from sources out of the FoI, but the drawback is that sources at the edges of the FoI will be smeared (Lonsdale et al 2004;Atemkeng et al 2016). However, increasing the SNR based on averaging is feasible only if both the FoI and its edges are preserved from smearing, and sources out of the FoI are suppressed.…”

“…The idea of BDA is thus not novel, and has also been subject of discussion in many radio interferometry conferences, particularly the ability to use BDA for the SKA data processors. Atemkeng et al (2016) discussed a baselinedependent window functions (BDWFs) scheme that has the effect to shape the FoI. Several other techniques to shape the FoI using window functions have been proposed (Lonsdale et al 2004;Parsons & Backer 2009;Parsons et al 2016).…”

Baseline-dependent averaging in radio interferometry

“…BDA has also been used for MWA, which initially had to operate with stringent storage capacity restrictions (Mitchell et al 2008). Besides data compression, BDA can also be used to shape the field-of-interest (Atemkeng et al 2016).…”