Before revision:  We give the first provable algorithms that work regardless of the separation, but only for a constant number of point sources. Surprisingly, we show that when the number of point sources becomes large, there is a phase transition where the sample complexity goes from polynomial to exponential , and we pin down its location to within a universal constant that is independent of the number of point sources.
After revision:  In particular we show that when the number of point sources becomes large, there is a phase transition where the sample complexity goes from polynomial to exponential , and we pin down its location to within a universal constant that is independent of the number of point sources.