# VLBI imaging of black holes via second moment regularization

## TL;DR

This paper introduces a second moment regularization technique for VLBI imaging that improves the reconstruction of extended features in black hole images by compensating for sparse short-baseline coverage.

## Contribution

The proposed method enforces a size constraint on the reconstructed image, enabling recovery of lost information and correction of systematic offsets in VLBI black hole imaging.

## Key findings

- Enhances imaging of extended features in black hole images.
- Allows size constraints from historical or multi-wavelength data.
- Effective for static and dynamic source reconstructions.

## Abstract

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.