Although it is not a main point in this paper, the computational efficiency is also a crucial challenge for the 3-D extension. As the image gathers become 5-D, the cost of wave-equation operators grows extremely fast as the problem size scales up.
Besides choosing a smaller model space, phase-encoded shot records can be used to reduce the number of wave-field simulations. The other bottle neck is the huge amount of disk IO when doing the cross-correlation imaging condition for many subsurface offsets. Based on the recently emerging research topic of compressive sensing, Clapp (2011) proposes a promising idea to reduce the amount of IO required. The author shows that if we randomly compute only a subset of the original full 5-D image, for typical seismic data, we can confidently recover the full image without losing useful information.