SUMMARYSeismic acquisition is confined by limited aperture that leads to finite illumination, which, together with other factors, hinders imaging of subsurface objects in complex geological settings such as salt structures. Conventional processing, including surface-related multiple elimination, further reduces the amount of information we can get from seismic data. With the growing consensus that multiples carry valuable information that is missing from primaries, we are motivated to exploit the extra illumination provided by multiples to image the subsurface. In earlier research, we proposed such a method by combining primary estimation and sparsity-promoting migration to invert for model perturbations directly from the total up-going wavefield. In this abstract, we focus on a particular case. By exploiting the extra illumination from surface-related multiples, we mitigate the effects caused by migrating from incomplete data with missing sources and missing near-offsets.