In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured subject to unknown permutations.
Previous work has leveraged the vertical nature of the edge to demonstrate 1D (in angle measured around the corner) reconstructions of moving and stationary hidden scenery from as little as a single photograph of the penumbra.
In this article, we study the convergence of Mirror Descent (MD) and Optimistic Mirror Descent (OMD) for saddle point problems satisfying the notion of coherence as proposed in Mertikopoulos et al. We prove convergence of OMD with exact gradients for coherent saddle point problems, and show that monotone convergence only occurs after some sufficiently large number of iterations.
The problem of reconstructing an object from the measurements of the light it scatters is common in numerous imaging applications.