Dynamic interpolation on Riemannian manifolds: an application to interferometric imaging

In this paper we derive necessary conditions for minimizing the cost function for a trajectory that evolves on a Riemannian manifold and satisfies a second order differential equation together with some interpolation, smoothness and motion constraints. The cost function we consider in this paper is a weighted sum of the norm squared of the acceleration and the norm squared of the velocity and is motivated by space-based interferometric imaging applications. In our current work, we define the dynamic interpolation problem, derive necessary conditions for an optimal solution and point out an interesting connection between the dynamic interpolation problem and imaging applications, which is the main contribution of this paper.