  Radio interferometry allows astronomers to probe small spatial scales that
are often inaccessible with single-dish instruments. However, recovering the
radio sky from an interferometer is an ill-posed deconvolution problem that
astronomers have worked on for half a century. More challenging still is
achieving resolution below the array's diffraction limit, known as
super-resolution imaging. To this end, we have developed a new learning-based
approach for radio interferometric imaging, leveraging recent advances in the
classical computer vision problems of single-image super-resolution (SISR) and
deconvolution. We have developed and trained a high dynamic range residual
neural network to learn the mapping between the dirty image and the true radio
sky. We call this procedure POLISH, in contrast to the traditional CLEAN
algorithm. The feed forward nature of learning-based approaches like POLISH is
critical for analyzing data from the upcoming Deep Synoptic Array (DSA-2000).
We show that POLISH achieves super-resolution, and we demonstrate its ability
to deconvolve real observations from the Very Large Array (VLA).
Super-resolution on DSA-2000 will allow us to measure the shapes and
orientations of several hundred million star forming radio galaxies (SFGs),
making it a powerful cosmological weak lensing survey and probe of dark energy.
We forecast its ability to constrain the lensing power spectrum, finding that
it will be complementary to next-generation optical surveys such as Euclid.
