We consider the following recovery problem: we have a discrete quasi-periodic subset X of Euclidean space, and we randomly perturb the points of X. Under which conditions can we recover X given a single observation of the perturbed set, almost surely? We look for sufficient conditions on the random perturbations to ensure this recovery. The problem for the case of independent identically distributed perturbations and for X a lattice, was solved by Yakir in 2020. The work presented here, done in collaboration with Rodolfo Viera (post-doc at PUC Chile), extends the theory to quasi-periodic X, and to more general random perturbations. If time allows, I will present some open questions as well.