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.