MULTI-PARAMETER TIKHONOV REGULARIZATION FOR LINEAR ILL-POSED OPERATOR EQUATIONS

We consider solving linear ill-posed operator equations.Based on a multi-scale decompositionfor the solution space,we propose a multi-parameter regularization for solving theequations.We establish weak and strong convergence theorems for the multi-parameterregularization solution.In particular,based on the eigenfunction decomposition,we developa posteriori choice strategy for multi-parameters which gives a regularization solutionwith the optimal error bound.Several practical choices of multi-parameters are proposed.We also present numerical experiments to demonstrate the outperformance of the multiparameterregularization over the single parameter regularization.