In this work, we present another proof of the theoretical existence of super resolution, under certain conditions. The proof relies on an ideal model in which a prototypical discrete image is formed by summation of many discrete pulses placed anywhere on a regular grid. If the model is then band-limited in spatial frequency, the original, grid-resolution pulse image may be reconstructed from the band-limited information. The reconstruction uses “phase-gradient unravelling” — i.e., from a very limited number of terms of the discrete Fourier transform of an image, which defines a very limited spatial-frequency band, we extract or unravel the individual phase-gradients which, together, define the original image.