On the reconstructability of images sampled by random line projections

This paper addresses the problem of sampling a two dimensional function (an image) by projections along lines with an arbitrary geometry. By usage of the Papoulis Generalized Sampling Expansion theorem, and addressing the problem of missing samples, we are able to state, for any given sampling realization, which sampling schemes will yield reconstructable images and what sampling (Nyquist) frequency is required for this realization. Finally, we apply this technique on two examples, and demonstrate that with certain geometries the function is reconstructable, while with others it is not.