Super-resolution of point sources in noisy images

The recovery of a superposition of (analog) point sources, at arbitrary locations "off the grid", in noisy (discrete) images. This is a recent field of research, with active people from the compressed sensing community (E. Candès, R. Baraniuk...) and from sampling theory (M. Vetterli, Y. Eldar...), among others. The range of applications is broad (astronomical imaging, confocal microscopy...). The main challenge is to extend recent results from 1D to 2D, which is far from trivial.