  We propose a new variational model for joint image reconstruction and motion
estimation in spatiotemporal imaging, which is investigated along a general
framework that we present with shape theory. This model consists of two
components, one for conducting modified static image reconstruction, and the
other performs sequentially indirect image registration. For the latter, we
generalize the large deformation diffeomorphic metric mapping framework into
the sequentially indirect registration setting. The proposed model is compared
theoretically against alternative approaches (optical flow based model and
diffeomorphic motion models), and we demonstrate that the proposed model has
desirable properties in terms of the optimal solution. The theoretical
derivations and efficient algorithms are also presented for a time-discretized
scenario of the proposed model, which show that the optimal solution of the
time-discretized version is consistent with that of the time-continuous one,
and most of the computational components is the easy-implemented linearized
deformation. The complexity of the algorithm is analyzed as well. This work is
concluded by some numerical examples in 2D space + time tomography with very
sparse and/or highly noisy data.
