Imaging with multiples accelerated by message passing

With the growing realization that multiples can provide valuable information, there is a paradigm shift from removing them to using them. For instance, primary estimation by sparse inversion has demonstrated its superiority over surface-related multiple removal in many aspects. Inspired by this shift, we propose a method to image directly from the total up-going wavefield, including surface-related multiples, by sparse inversion. To address the high computational cost associated with this method, we propose to speed up the inversion by having the wave-equation solver carry out the multi-dimensional convolutions implicitly and cheaply by randomized subsampling. We improve the overall performance of this algorithm by selecting new independent copies of the randomized modeling operator, which leads to a cancellation of correlations that hamper the speed of convergence of the solver. We show the merits of our approach on a number of examples.