The w-effect in interferometric imaging: from a fast sparse measurement operator to super-resolution

Arwa Dabbech, Laura Wolz, Luke Prateley, Jason D. McEwen, Yves Wiaux

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
83 Downloads (Pure)


Modern radio telescopes, such as the Square Kilometre Array (SKA), will probe the radio sky over large fields-of-view, which results in large w-modulations of the sky image. This effect complicates the relationship between the measured visibilities and the image under scrutiny. In algorithmic terms, it gives rise to massive memory and computational time requirements. Yet, it can be a blessing in terms of reconstruction quality of the sky image. In recent years, several works have shown that large w-modulations promote the spread spectrum effect. Within the compressive sensing framework, this effect increases the incoherence between the sensing basis and the sparsity basis of the signal to be recovered, leading to better estimation of the sky image. In this article, we revisit the w-projection approach using convex optimisation in realistic settings, where the measurement operator couples the w-terms in Fourier and the de-gridding kernels. We provide sparse, thus fast, models of the Fourier part of the measurement operator through adaptive sparsification procedures. Consequently, memory requirements and computational cost are significantly alleviated, at the expense of introducing errors on the radio-interferometric data model. We present a first investigation of the impact of the sparse variants of the measurement operator on the image reconstruction quality. We finally analyse the interesting super-resolution potential associated with the spread spectrum effect of the w-modulation, and showcase it through simulations. Our C++ code is available online on GitHub.
Original languageEnglish
Pages (from-to)4300–4313
Number of pages14
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
Early online date14 Jul 2017
Publication statusPublished - 11 Nov 2017


  • Image processing
  • techniques: interferometric


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