Super-Resolution of Positive Sources on an Arbitrarily Fine Grid

Understand

In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c.

• In the case when the point sources are positive and are located on a grid, it has been recently established that the super-resolution problem can be solved via linear programming in a stable manner and that the method is nearly optimal in the minimax sense.
• The quality of the reconstruction critically depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within an interval of side length about 1/f_c.
• This work extends the earlier result and shows that the conclusion continues to hold when the locations of the point sources are arbitrary, i.e., the grid is arbitrarily fine.