  The aim of this paper is to derive and analyze a variational model for the
joint estimation of motion and reconstruction of image sequences, which is
based on a time-continuous Eulerian motion model. The model can be set up in
terms of the continuity equation or the brightness constancy equation. The
analysis in this paper focuses on the latter for robust motion estimation on
sequences of two-dimensional images. We rigorously prove the existence of a
minimizer in a suitable function space setting. Moreover, we discuss the
numerical solution of the model based on primal-dual algorithms and investigate
several examples. Finally, the benefits of our model compared to existing
techniques, such as sequential image reconstruction and motion estimation, are
shown.
