Brief explanation of the problem:

Estimation of single peak solving a L1-norm convex optimization problem on a discrete grid are presented here.

The support of the underlying sparse signal is not on the grid.

The de-convoluted signal yields pairs of peaks on the grid points which are adjacent to the location of the original peak.

These pairs of peaks can be used to extrapolate the location of the actual peak.

A video that shows how superresolution is performed using simulated 2D florescence data.

This is an ongoing research so further examples will appear soon.....