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E. Klann, P. Maa, R. Ramlau

Two-step regularization methods for linear inverse problems

In this paper we investigate reconstruction methods for the treatment of ill-posed inverse problems. These methods are based on a data estimation operator S_λ followed by a classical regularization operator R_α

T_α,λ = R_αS_λ.

As a particular example of such a two-step regularization method we investigate in detail the combination of a wavelet shrinkage operator S_λ followed by Tikhonov regularization R_α.

The nonlinear shrinkage operator is applied to noisy data and partially recovers the smoothness properties of the exact data. We prove order optimality for the proposed scheme and confirm the theoretical results with an example from medical imaging.

Journal of Inverse and Ill-posed Problems, Walter de Gruyter

Print ISSN: 0928-0219
Volume: 14, 09/2006
Pages: 583 - 607

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