Saturation spaces for regularization methods in inverse problems

The aim of this article is to characterize the saturation spaces that appear in inverse problems. Such spaces are defined for a regularization method and the rate of convergence of the estimation part of the inverse problem depends on their definition. Here we prove that it is possible to define these spaces as regularity spaces, independent of the choice of the approximation method. Moreover, this intrinsec definition enables us to provide minimax rate of convergence under such assumptions