The convergence of a new heuristic parameter selection criterion for general regularization methods

In this paper we derive convergence and convergence rates results for a new parameter selection criterion for regularization methods based on spectral theory when applied to linear ill-posed problems Tx = y. We prove convergence and suboptimal rates under a qualitative condition on the decay of the noise with respect to the spectral family of TT*. Moreover, optimal rates are obtained if the exact solution satisfies a decay condition with respect to the spectral family of T*T.