We discuss a new regularization scheme for reconstructing the solution of a
linear ill-posed operator equation from given noisy data in the Hilbert space
setting. In this new scheme, the regularized approximation is decomposed
into several components, which are defined by minimizing a multi-penalty
functional. We show theoretically and numerically that under a proper choice
of the regularization parameters, the regularized approximation exhibits the
so-called compensatory property, in the sense that it performs similar to the
best of the single-penalty regularization with the same penalizing operator.