SUMMARYObtaining seismic images of the subsurface near and beneath salt is very difficult due to seismic energy that is lost by propagating outside of the survey area or becoming evanescent at salt boundaries (poor illumination). We demonstrate an iterative regularized least-squares inversion for imaging that helps to compensate for illumination problems. We show the use of a regularization operator that acts to regularize amplitudes along reflection angles (or equivalent offset ray parameters) to compensate for the sudden, large amplitude changes caused by poor illumination. This regularization operator has the effect of filling in the gaps created in the reflection angle range due to the lost seismic energy. We discuss the use of this regularization operator in an iterative least-squares inversion scheme to improve imaging for a poorly illuminated 3-D seismic dataset. We introduce a new type of joint inversion problem that will allows us to simultaneously invert two or more datasets. For this iterative inversion scheme, we design a different regularization operator that allows us to share illumination information between images created from the different datasets involved. This regularized inversion allows us to create images that share the illumination information from the different datasets.