We propose an approach to correct the data of the airborne large-aperture static image spectrometer (LASIS). LASIS is a kind of stationary interferometer which compromises flux output and device stability. It acquires a series of interferograms to reconstruct the hyperspectral image cube. Reconstruction precision of the airborne LASIS data suffers from the instability of the plane platform. Usually, changes of plane attitudes, such as yaws, pitches, and rolls, can be precisely measured by the inertial measurement unit. However, the along-track and across-track translation errors are difficult to measure precisely. To solve this problem, we propose a co-optimization approach to compute the translation errors between the interferograms using an image registration technique which helps to correct the interferograms with subpixel precision. To demonstrate the effectiveness of our approach, experiments are run on real airborne LASIS data and our results are compared with those of the state-of-the-art approaches.