Approximating W projection as a separable kernel

TL;DR

This paper demonstrates that W projection kernels in interferometric imaging can be closely approximated by separable kernels, significantly reducing storage needs while maintaining accuracy for high-resolution wide-field imaging.

Contribution

The authors introduce a method to approximate W projection kernels as separable kernels, enabling more efficient storage and computation in interferometric imaging.

Findings

Separable kernels closely approximate W projection kernels with minimal error.

Error scales with the fourth power of the field of view, remaining small at high frequencies.

Hybrid algorithms further reduce approximation error, suitable for high-resolution wide-field instruments.

Abstract

W projection is a commonly-used approach to allow interferometric imaging to be accelerated by Fast Fourier Transforms (FFTs), but it can require a huge amount of storage for convolution kernels. The kernels are not separable, but we show that they can be closely approximated by separable kernels. The error scales with the fourth power of the field of view, and so is small enough to be ignored at mid to high frequencies. We also show that hybrid imaging algorithms combining W projection with either faceting, snapshotting, or W stacking allow the error to be made arbitrarily small, making the approximation suitable even for high-resolution wide-field instruments.