The problem of interpolating an image from a downsampled version is investigated. In particular, prior knowledge of the statistics of the data and measurement noise, as well as the method of sampling, are shown to lead to an optimal interpolator. The availability of SPOT satellite image data sampled at two resolutions, one twice that of the other, provides a basis for the study. Firstly a direct inverse filter is derived from the satellite data. Secondly, interpolators based on models for the auto-covariance of the higher resolution data are derived and an equivalence for these and the direct type is shown. Thirdly a comparison of the spectra of the interpolators reveals that both the inverse and statistical interpolators give significant boost to frequencies below the nominal bandlimit and that their response is significant at frequencies above but adjacent to the nominal bandlimit. Finally, numerical studies indicate that when the prior knowledge is accurate there is less residual mean square error associated with the direct and statistical interpolators, compared to a sinc-based interpolator.