Accurate information on the ice thickness of Svalbard's glaciers is important for assessing the contribution to sea level rise in a present and a future climate. However, direct observations of the glacier bed are scarce. Here, we use an inverse approach and high-resolution surface observations to infer basal conditions. We present and analyse the new bed and thickness maps, quantify the ice volume (6800 km³), and compare these against radar data and previous studies.