Bayesian wavefield separation by transform-domain sparsity promotion

Conclusions

In this letter, we introduce a robust algorithm for the separation of coherent signal components that are sparse in the same transform domain. The separation problem is formulated in terms of Bayesian statistics where curvelet-domain sparsity and approximate independence of the to-be-separated signal components both serve as priors. Given initial predictions of signal components that contain moderate errors, the proposed algorithm outputs improved estimates of these components. Convergence of our separation algorithm is assured by defining the weighted one-norms of the signal components in terms of the initial signal predictions that serve as input. The fast convergence and the quality of the separation results both follow from the ability of curvelets to sparsely represent each signal component. This observation opens the tantalizing perspective of a generic algorithm where coherent signal components are successfully separated, given signal predictions with moderate errors. Our excellent results on primary-multiple separation seem to underline this perspective.