A distributed resource-adaptive implementation of the wideband widefield radio-interferometric measurement model

Modern radio-interferometric (RI) arrays target imaging the radio sky at extreme resolutions and dynamic ranges. However, processing the sheer volumes of wideband data typically generated during observation poses significant computational challenges. Moreover, for widefield imaging, the baseline components 𝑤 along the line of sight introduce measurement-dependent phase modulations that severely complicate the measurement model beyond the conventional 2-dimensional non-uniform Fourier transform. To incorporate this effect accurately, the widely used 𝑤-stacking approach groups data into numerous finely-sampled 𝑤-bins, requiring as many Fourier transforms, at the expense of a high computational cost. Alternatively, the 𝑤-projection approach encodes the modulations via large Fourier convolutional kernels, requiring a single Fourier transform but at the expense of significant memory demands. We propose a distributed resource-adaptive implementation of the wideband widefield RI measurement model, underpinned by a hybrid 𝑤-stacking/𝑤-projection approach optimising the trade-off between computational and memory requirements in a fully automated manner. The resulting measurement operator Φ and its adjoint Φ^† enable fast computation of the dirty image Φ^†𝒚 from the data 𝒚 and its modelling Φ^†Φ𝒙 from an image 𝒙. These operations are core to image formation with any iterative algorithm, from CLEAN, SARA, and RESOLVE, to AIRI or R2D2. An option for data dimensionality reduction is also proposed, whereby the Fourier de-gridding operation of Φ and the gridding operation of Φ^† will be automatically encoded into a holographic matrix if required by memory constraints. We demonstrate the efficiency of the framework using simulated 20GB-scale MeerKAT data. A MATLAB implementation is available in BASPLib.