Recently, new sampling schemes were presented for signals with finite rate of innovation (FRI) using sampling kernels reproducing polynomials or exponentials. In this paper, we extend those sampling schemes to a distributed acquisition architecture in which numerous and randomly located sensors are pointing to the same area of interest. We emphasize the importance played by moments and show how to acquire efficiently FRI signals with a set of sensors. More importantly, we also show that those sampling schemes can be used for accurate registration of affine transformed and low-resolution images. Based on this, a new super-resolution a