Measuring a large set of room impulse responses inside a volume of interest is time-consuming unless a large number of microphones is involved. However, increasing the number of microphones requires more hardware and raises effort, e.g., in calibration. Instead of measuring at any desired position, it is possible to spatially interpolate the sound field between sampled positions, in order to obtain estimates at unknown positions. Nevertheless, the Nyquist-Shannon sampling theorem should be met, which still demands a large number of spatial sampling points for large bandwidths. In this paper, we present a compressed-sensing approach that allows for stable and robust interpolation of room impulse responses using less measurements than required by the sampling theorem. Based on a small set of spatially subsampled room impulse responses, the proposed method is capable of providing an enlarged set allowing for aliasing- free reconstruction in space.