Recovering the Wedge Modes Lost to 21-cm Foregrounds

Abstract: One of the critical challenges facing imaging studies of the 21-cm signal at the Epoch of Reionization (EoR) is the separation of astrophysical foreground contamination. These foregrounds are known to lie in a wedge-shaped region of $(k_{\perp},k_{\parallel})$ Fourier space. Removing these Fourier modes excises the foregrounds at grave expense to image fidelity, since the cosmological information at these modes is also removed by the wedge filter. However, the 21-cm EoR signal is non-Gaussian, meaning that the lost wedge modes are correlated to the surviving modes by some covariance matrix. We have developed a machine learning-based method which exploits this information to identify ionized regions within a wedge-filtered image. Our method reliably identifies the largest ionized regions and can reconstruct their shape, size, and location within an image. We further demonstrate that our method remains viable when instrumental effects are accounted for, using the Hydrogen Epoch of Reionization Array and the Square Kilometre Array as fiducial instruments. The ability to recover spatial information from wedge-filtered images unlocks the potential for imaging studies using current- and next-generation instruments without relying on detailed models of the astrophysical foregrounds themselves.