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On Tikhonov-type regularization with approximated penalty terms

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  • In this paper, we deal with (nonlinear) ill-posed problems that are regularized by minimizing Tikhonov-type functionals. If the minimization is tedious for some penalty term $ P_0 $, we approximate it by a family of penalty terms $ ({P_\beta}) $ having nicer properties and analyze what happens as $ \beta\to 0 $.

    We investigate the discrepancy principle for the choice of the regularization parameter and apply all results to linear problems with sparsity constraints. Numerical results show that the proposed method yields good results.

    Mathematics Subject Classification: Primary: 47J06, 47A52; Secondary: 65J20.


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  • Figure 1.  Exact solution and reconstructions for noise level $ \delta = 1 $%

    Figure 2.  Exact solution and reconstructions for noise level $ \delta = 10 $%

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