  In a number of astrophysical applications one tries to determine the
two-dimensional or three-dimensional structure of an object from a time series
of measurements. While most methods used for reconstruction assume that object
is static, the data are often acquired over a time interval during which the
object may change significantly. This problem may be addressed with
time-dependent reconstruction methods such as Kalman filtering which models the
temporal evolution of the unknown object as a random walk that may or may not
have a deterministic component. Time-dependent reconstructions of a
hydrodynamical simulation from its line-integral projections are presented. In
these examples standard reconstructions based on the static assumption are poor
while the Kalman based reconstructions are of good quality. Implications for
various astrophysical applications, including tomography of the solar corona
and radio aperture synthesis, are discussed.
