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Convergence of regularization methods with filter functions for a regularization parameter chosen with GSURE and mildly ill-posed inverse problems

Bruno Sixou 1 
1 Imagerie Tomographique et Radiothérapie
CREATIS - Centre de Recherche en Acquisition et Traitement de l'Image pour la Santé
Abstract : In this work, we show that the regularization methods based on filter functions with a regularization parameter chosen with the GSURE principle are convergent for mildly ill-posed inverse problems and under some smoothness source condition. The convergence rate of the methods is not optimal for very ill-posed problems but the efficiency increases with the smoothness of the solution
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Bruno Sixou. Convergence of regularization methods with filter functions for a regularization parameter chosen with GSURE and mildly ill-posed inverse problems. Journal of Computational and Applied Mathematics, 2020, 378, pp.112938. ⟨10.1016/j.cam.2020.112938⟩. ⟨hal-02954647⟩

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