Most of the data acquisition in ground-penetrating radar is done along fixed-offset profiles, in which velocity is known only at isolated points in the survey area, at the locations of variable offset gathers such as a common midpoint. We have constructed sparse, heavily aliased, variable offset gathers from several fixed-offset, collinear, profiles. We interpolated those gathers to produce properly sampled counterparts, thus pushing data beyond aliasing. The interpolation methodology estimated nonstationary, adaptive, filter coefficients at all trace locations, including at the missing traces’ corresponding positions, filled with zeroed traces. This is followed by an inversion problem that uses the previously estimated filter coefficients to insert the new, interpolated, traces between the original ones. We extended this two-step strategy to data interpolation by employing a device in which we used filter coefficients from a denser variable offset gather to interpolate the missing traces on a few independently constructed gathers. We applied the methodology on synthetic and real data sets, the latter acquired in the interior of the Antarctic continent. The variable-offset interpolated data opened the door to prestack processing, making feasible the production of a prestack time migrated section and a 2D velocity model for the entire profile. Notwithstanding, we have used a data set obtained in Antarctica; there is no reason the same methodology could not be used somewhere else.