  Very long baseline interferometry (VLBI) makes it possible to recover images
of astronomical sources with extremely high angular resolution. Most recently,
the Event Horizon Telescope (EHT) has extended VLBI to short millimeter
wavelengths with a goal of achieving angular resolution sufficient for imaging
the event horizons of nearby supermassive black holes. VLBI 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 (Sgr A*) targeted by the
EHT, this assumption is violated and these conventional imaging approaches
fail. In this work we propose a new way to model VLBI measurements that allows
us to recover 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, we are able to propagate
information across observations in time to reconstruct a video, while
simultaneously learning about the dynamics of the source's emission region. We
demonstrate our proposed Expectation-Maximization (EM) algorithm, StarWarps, on
realistic synthetic observations of black holes, and show how it substantially
improves results compared to conventional imaging algorithms. Additionally, we
demonstrate StarWarps on real VLBI data of the M87 Jet from the VLBA.
