Self-Calibrated Super Resolution

Super-resolution source localization is a fundamental problem in many sensing and imaging applications, where the goal is to identify the location of point sources from its convolution with a low-pass point spread function. Most super resolution algorithms assume perfect knowledge or stringent assumptions on the point spread function, and deliver highly inaccurate localizations when the point spread function is unknown or ill-calibrated. In this paper, we consider the problem of blind super resolution, with the goal of making almost no assumptions on the structures of the point spread function, by leveraging the availability of multi-channel observations. Specifically, we propose a novel algorithm based on atomic norm minimization, a recent convex optimization framework for super resolution, and demonstrate its success through extensive numerical experiments. Moreover, the optimality condition of the proposed estimator is studied.