Ice thickness data over much of East Antarctica are sparse and irregularly distributed. This poses difficulties for reconstructing the homogeneous coverage needed to properly assess underlying sub-glacial morphology and fundamental geometric constraints on sea level rise. Here we introduce a new physically-based ice thickness interpolation scheme and apply this to existing ice thickness data in the Aurora Subglacial Basin region. The skill and robustness of the new reconstruction is demonstrated by comparison with new data from the ICECAP project. The interpolated morphology shows an extensive marine-based ice sheet, with considerably more area below sea-level than shown by prior studies. It also shows deep features connecting the coastal grounding zone with the deepest regions in the interior. This has implications for ice sheet response to a warming ocean and underscores the importance of obtaining additional high resolution data in these marginal zones for modelling ice sheet evolution.