Multi-penalty regularization with a component-wise penalization

V Naumova, S V Pereverzyev
2013 Inverse Problems  
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
more » ... that it performs similar to the best of the single-penalty regularization with the same penalizing operator.
doi:10.1088/0266-5611/29/7/075002 fatcat:y3y6y32kqbezlnryigszm7g4xe