  By linking widely separated radio dishes, the technique of very long baseline
interferometry (VLBI) can greatly enhance angular resolution in radio
astronomy. However, at any given moment, a VLBI array only sparsely samples the
information necessary to form an image. Conventional imaging techniques
partially overcome this limitation by making the assumption that the observed
cosmic source structure does not evolve over the duration of an observation,
which enables VLBI networks to accumulate information as the Earth rotates and
changes the projected array geometry. Although this assumption is appropriate
for nearly all VLBI, it is almost certainly violated for submillimeter
observations of the Galactic Center supermassive black hole, Sagittarius A*
(Sgr A*), which has a gravitational timescale of only ~20 seconds and exhibits
intra-hour variability. To address this challenge, we develop several
techniques to reconstruct dynamical images ("movies") from interferometric
data. Our techniques are applicable to both single-epoch and multi-epoch
variability studies, and they are suitable for exploring many different
physical processes including flaring regions, stable images with small
time-dependent perturbations, steady accretion dynamics, or kinematics of
relativistic jets. Moreover, dynamical imaging can be used to estimate
time-averaged images from time-variable data, eliminating many spurious image
artifacts that arise when using standard imaging methods. We demonstrate the
effectiveness of our techniques using synthetic observations of simulated black
hole systems and 7mm Very Long Baseline Array observations of M87, and we show
that dynamical imaging is feasible for Event Horizon Telescope observations of
Sgr A*.
