"Off-the-Grid Estimation of Singular Measures"
Catala, PaulMany problems in imaging science involve reconstructing, from partial observations, highly concentrated signals, e.g. pointwise sources or contour lines. We consider in this work the problem of recovering measures supported on such singular sets, given finitely many of their trigonometric moments. We introduce simple polynomial estimates, and prove pointwise and weak convergence as the number $n$ of known moments increases. We show that the optimal weak convergence rate with respect to the Wasserstein-1-distance is inversely proportional to $n$, and that it is achieved by our estimate.