  Observing the dynamics of compact astrophysical objects provides insights
into their inner workings, thereby probing physics under extreme conditions.
The immediate vicinity of an active supermassive black hole with its event
horizon, photon ring, accretion disk, and relativistic jets is a perfect place
to study general relativity and magneto-hydrodynamics. The observations of M87*
with Very Long Baseline Interferometry (VLBI) by the Event Horizon Telescope
(EHT) allows to investigate its dynamical processes on time scales of days.
Compared to regular radio interferometers, VLBI networks typically have fewer
antennas and low signal to noise ratios (SNRs). Furthermore, the source is
variable, prohibiting integration over time to improve SNR. Here, we present an
imaging algorithm that copes with the data scarcity and temporal evolution,
while providing uncertainty quantification. Our algorithm views the imaging
task as a Bayesian inference problem of a time-varying brightness, exploits the
correlation structure in time, and reconstructs a ${2+1+1}$ dimensional
time-variable and spectrally resolved image at once. We apply this method to
the EHT observation of M87* and validate our approach on synthetic data. The
time- and frequency-resolved reconstruction of M87* confirms variable
structures on the emission ring. The reconstruction indicates extended and
time-variable emission structures outside the ring itself.
