S-R2D2: a spherical extension of the R2D2 deep neural network series paradigm for wide-field radio-interferometric imaging
This work addresses the spherical-imaging requirement for modern radio telescopes observing wide fields, which is a domain-specific problem in radio astronomy, and represents an incremental extension of the existing R2D2 paradigm.
The paper tackles the limitation of the R2D2 deep neural network paradigm, which is restricted to planar imaging for radio interferometry, by proposing S-R2D2, a spherical extension that enables wide-field imaging on the sphere. The result is a method that performs fast and accurate reconstructions of spherical monochromatic intensity images in high-resolution, high-dynamic-range settings, as demonstrated through simulations.
Recently, the R2D2 paradigm, standing for ''Residual-to-Residual DNN series for high-Dynamic-range imaging'', was introduced for image formation in Radio Interferometry (RI) as a learned version of the traditional algorithm CLEAN. The first incarnations of R2D2 are limited to planar imaging on small fields of view, failing to meet the spherical-imaging requirement of modern telescopes observing wide fields. To address this limitation, we propose the spherical-imaging extension S-R2D2. Firstly, as R2D2, S-R2D2 encapsulates its minor cycles in existing 2D-Euclidean deep neural network (DNN) architectures, but adapts its iterative scheme to incorporate the wide-field measurement model mapping a spherical image to visibility data. We implemented this model as the composition of an efficient Fourier-based interpolator mapping the spherical image onto the equatorial plane, with the standard RI operator mapping the equatorial-plane image to visibility data. Importantly, the interpolation step must inevitably be performed at a lower-than-optimal resolution on the plane, to meet the high-resolution requirement on the sphere of wide-field imaging while preserving scalability. Therefore, secondly, we design S-R2D2's DNN training loss to jointly learn to correct the interpolation approximations and identify residual image structures on the sphere, ensuring consistency with the spherical ground truth using the adjoint plane-to-sphere interpolator. Finally, we demonstrate through simulations S-R2D2's capability to perform fast and accurate reconstructions of spherical monochromatic intensity images, across high-resolution, high-dynamic-range settings.