Bayesian wavefield separation by transform-domain sparsity promotion

Theory

The proposed method involves the separation of two (or more since our method extends to more than two signal components) coherent signal components, given a prediction for one of the signal components. In SRME, this problem corresponds to separating primaries and multiples, given a prediction for the multiples with moderate errors. To solve this problem, we present a Bayesian formulation that allows for errors in the total data as well as in the predicted noise component. Without loss of generality, the ensuing discussion is limited to the problem of primary-multiple separation, where the total data and predicted multiples serve as input and during which estimates for the primaries and multiples are calculated. The predicted multiples are assumed to be given by the matched filter of standard SRME, possibly supplemented by a curvelet-domain matched filter recently proposed by Herrmann et al. (2007b).