Reconstructing Video of Time-Varying Sources From Radio Interferometric Measurements

Very long baseline interferometry (VLBI) makes it possible to recover the images of astronomical sources with extremely high angular resolution. Most recently, the Event Horizon Telescope (EHT) has extended VLBI to short millimeter wave-lengths with a goal of achieving angular resolution sufficient for imaging the event horizons of nearby supermassive black holes. Interferometry provides measurements related to the underlying source image through a sparse set spatial frequencies. An image can then be recovered from these measurements by making assumptions about the underlying image. One of the most important assumptions made by conventional imaging methods is that over the course of a night's observation the image is static. However, for quickly evolving sources, such as the galactic center's supermassive black hole (SgrA*) targeted by the EHT, this assumption is violated and these conventional imaging approaches fail. This paper presents a new way to model VLBI measurements that allows for the recovery of both the appearance and dynamics of an evolving source by reconstructing a video rather than a static image. By modeling VLBI measurements using a Gaussian Markov Model, information can be propagated across observations in time to reconstruct a video, while simultaneously learning about the dynamics of the source's emission region. This paper demonstrates our proposed expectation-maximization algorithm, Star Warps, on realistic synthetic observations of black holes, and shows how it substantially improves the results compared to conventional imaging methods. In addition to synthetic data, the technique is demonstrated on real VLBA data of the M87 jet.