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Multi-penalty regularization with a component-wise penalization
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 sensedoi:10.1088/0266-5611/29/7/075002 fatcat:y3y6y32kqbezlnryigszm7g4xe