Unified convex optimization approach to super-resolution based on localized kernels

The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings. We suggest a unified convex optimization approach for super-resolution. The key is the construction of an interpolating polynomial in the measurements space based on localized kernels. We also show that the localized kernels act as the connecting thread to another wide-spread problem of stream of pulses.