Subsalt imaging is a difficult but increasingly important problem. The poor illumination that occurs when seismic energy is affected by the complex subsurface at and around salt bodies causes significant shadow zones in migration results. These shadow zones may contain real signal, but it is weak compared to the artifacts caused by multipathing and poor illumination. To reduce artifacts and recover this energy, thereby improving the image, we use an imaging (migration) operator in a regularized least-squares inversion. The regularization operator acts on the offset ray parameter (reflection angle) axis of the model space. Performing several iterations of regularized inversion that penalize large changes along the offset ray parameter axis results in an image with recognizable events in the shadow zones and fewer artifacts. We perform regularized inversion with model preconditioning on real 2-D and 3-D data to obtain seismic images that are better in poorly illuminated areas than migration results.