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