Stabalized Estimation of Primaries by Sparse Inversion

Estimation of Primaries by Sparse Inversion (EPSI) is a recent method for surface-related multiple removal using a direct estimation method closely related to Amundsen inversion, where under a sparsity assumption the primary impulse response is determined directly from a data-driven wavefield inversion process. One of the major difficulties in its practical adoption is that one must have precise knowledge of a time-window that contains multiple-free primaries during each update. Moreover, due to the nuances involved in regularizing the model impulse response in the inverse problem, the EPSI approach has an additional number of inversion parameters where it may be difficult to choose a reasonable value. We show that the specific sparsity constraint on the EPSI updates lead to an inherently intractable problem, and that the time-window and other inversion variables arise in the context of additional regularizations that attempts to drive towards a meaningful solution. We furthermore suggest a way to remove almost all of these parameters via convexification, which stabilizes the inversion while preserving the crucial sparsity assumption in the primary impulse response model.