VLBI imaging of black holes via second moment regularization

The imaging fidelity of the Event Horizon Telescope (EHT) is currently determined by its sparse baseline coverage. In particular, EHT coverage is dominated by long baselines, and is highly sensitive to atmospheric conditions and loss of sites between experiments. The limited short/mid-range baselines especially affect the imaging process, hindering the recovery of more extended features in the image. We present an algorithmic contingency for the absence of well-constrained short baselines in the imaging of compact sources, such as the supermassive black holes observed with the EHT. This technique enforces a specific second moment on the reconstructed image in the form of a size constraint, which corresponds to the curvature of the measured visibility function at zero baseline. The method enables the recovery of information lost in gaps of the baseline coverage on short baselines and enables corrections of any systematic amplitude offsets for the stations giving short-baseline measurements present in the observation. The regularization can use historical source size measurements to constrain the second moment of the reconstructed image to match the observed size. We additionally show that a characteristic size can be derived from available short-baseline measurements, extrapolated from other wavelengths, or estimated without complementary size constraints with parameter searches. We demonstrate the capabilities of this method for both static and movie reconstructions of variable sources.