In this study, we apply the three-dimensional Stockwell Transform (3DST) to a novel dataset, namely airglow imager data from Rothera (68S, 68W). We use this approach to investigate small-scale high-frequency gravity waves (GWs) in the hydroxyl (OH) airglow layer, at a height $\sim$87 km in the mesosphere and lower thermosphere (MLT). MLT GWs are often underrepresented in models, being parameterised due to their small scale size and as such, the significant quantities of momentum and energy transferred by these small waves are missed. Better quantification of these waves is thus needed to support future model development. We find that the 3DST can identify waves and extract wave properties and their locations. Horizontal wavelengths are observed ranging from 10 to 40 km and vertical wavelengths of 15 to 40 km, with wave periods of 5 to 9 minutes, peaking at 7.5 minutes. These values are consistent with previous studies. Group speeds are found to be non-zero and large, implying that these GWs travel horizontally and fast. This case study demonstrates that the 3DST can be applied to airglow imager data and can successfully extract GW parameters. This is an important step in automating GW analysis in airglow.