A distributed resource-adaptive implementation of the widefield radio-interferometric measurement model for scalable image formation

Abstract

Modern image formation algorithms in radio interferometry rely on repeated applications of the operator Φ modelling the measurement process and its adjoint {Phi^\dagger} to enforce consistency with the acquired data, specifically via their composite mapping {Phi^\daggerΦ} encoding the array's point spread function (PSF). The large data volumes produced during wideband observations yield significant computational challenges for image formation. Moreover, for widefield imaging, the baseline components along the line of sight w complicate severely the measurement model beyond the conventional 2-dimensional non-uniform Fourier transform (NUFFT), making the PSF highly position-dependent. We propose a distributed resource-adaptive implementation of the widefield measurement model, enabled by a hybrid w-stacking/w-projection approach, whereby the number of w-bins is set in a fully automated manner to minimise the computational cost under the compute system's memory constraints. The resulting measurement model is naturally decomposed and distributed into low-dimensional operators specific to w-bins. Residual w-offsets are integrated as measurement-specific Fourier kernels augmenting the sparse de-gridding matrix of the basic NUFFT model. An optional data dimensionality reduction is also introduced, jointly encoding the sequential Fourier de-gridding/gridding operations in {Phi^\daggerΦ} into a holographic matrix when required by memory constraints. For further parallelisation, the sparse de-gridding or holographic matrices are decomposed into blocks via memory-controlled Fourier partitioning. The approach has been validated in prior works through real data case studies for both monochromatic and wideband imaging of MeerKAT and ASKAP data. We provide herein a thorough analysis of its computational efficiency using simulated MeerKAT data. A MATLAB implementation is available in BASPLib.