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

## TL;DR

This paper explores how the w-effect in interferometric imaging, especially with large w-modulations, can be modeled efficiently using sparse operators, enhancing super-resolution capabilities and reducing computational costs in radio astronomy imaging.

## Contribution

It introduces sparse, fast models of the measurement operator for interferometric imaging that leverage the spread spectrum effect for improved super-resolution, with analysis of their impact on reconstruction quality.

## Key findings

- Sparse models significantly reduce memory and computation.
- Large w-modulations enhance super-resolution potential.
- Sparse operators maintain acceptable image reconstruction quality.

## 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.