  The reconstruction of images from measured data is an increasing field of
research. For highly under-determined problems, template-based image
reconstruction provides a way of compensating for the lack of sufficient data.
A caveat of this approach is that dealing with different topologies of the
template and the target image is challenging. In this paper, we propose a
LDDMM-based image-reconstruction model that resolves this issue by adding a
source term. On the theoretical side, we show that the model satisfies all
criteria for being a well-posed regularization method. For the implementation,
we pursue a discretize-then-optimize approach involving the proximal
alternating linearized minimization algorithm, which is known to converge under
mild assumptions. Our simulations with both artificial and real data confirm
the robustness of the method, and its ability to successfully deal with
topology changes even if the available amount of data is very limited.
