I introduce the theory for compressed generalized diffraction-stack migration that is tuned to migrate multiple scattering events. A wavelet transform is used to compress both source-side and receiver-side Green's functions and a compression ratio of 10 is reached with a small loss of accuracy in the Green's functions. The computation time of the GDM is greatly reduced due to the compression of these Green's functions and a migration image with a higher lateral resolution is achieved by the use of multiple scattering. However, the compression ratio of 10 is still not enough for an efficient implementation of this method. I will assess the feasibility for efficiently implementing both the convolution and the dot-product in the wavelet domain instead of the time domain in the future. An important challenge in achieving superresolution images is how to estimate an accurate migration velocity model so that multiple scattering events can be properly focused.