Anti-alias Optimal Interpolation with Priors

We introduce a new technique referred to as Optimal Interpolation with Priors, or OIP, for interpolation of irregularly sampled signals, using prior estimates of their spectral content, which is optimal in the least square sense. In this paper, after introducing this technique and describing its basic advantages with respect to other state of the art regularization techniques, we demonstrate its potential to interpolate signals that are spatially aliased, based on realistic prior information. We also propose an algorithm to obtain a reliable prior estimate of the signal spectrum. The combined use of this algorithm and OIP, referred to henceforth as Anti-Alias OIP (AA-OIP), can be applied to datasets irregularly sampled in multi-dimensional spaces.