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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10277/703

Autori: Buccini, Alessandro
Tutor interno: DONATELLI, MARCO
Titolo: Tikhonov-type iterative regularization methods for ill-posed inverse problems: theoretical aspects and applications
Abstract: Ill-posed inverse problems arise in many fields of science and engineering. The ill-conditioning and the big dimension make the task of numerically solving this kind of problems very challenging. In this thesis we construct several algorithms for solving ill-posed inverse problems. Starting from the classical Tikhonov regularization method we develop iterative methods that enhance the performances of the originating method. In order to ensure the accuracy of the constructed algorithms we insert a priori knowledge on the exact solution and empower the regularization term. By exploiting the structure of the problem we are also able to achieve fast computation even when the size of the problem becomes very big. We construct algorithms that enforce constraint on the reconstruction, like nonnegativity or flux conservation and exploit enhanced version of the Euclidian norm using a regularization operator and different semi-norms, like the Total Variaton, for the regularization term. For most of the proposed algorithms we provide efficient strategies for the choice of the regularization parameters, which, most of the times, rely on the knowledge of the norm of the noise that corrupts the data. For each method we analyze the theoretical properties in the finite dimensional case or in the more general case of Hilbert spaces. Numerical examples prove the good performances of the algorithms proposed in term of both accuracy and efficiency.
Parole chiave: Regularization of ill-posed inverse problems, iterative regularization methods, image deblurring
MIUR : MAT/08 ANALISI NUMERICA
Data: 2016
Lingua: eng
Corso di dottorato: Informatica e matematica del calcolo
Ciclo di dottorato: 29
Università di conseguimento titolo: Università degli Studi dell'Insubria
Citazione: Buccini, A.Tikhonov-type iterative regularization methods for ill-posed inverse problems: theoretical aspects and applications (Doctoral Thesis, Università degli Studi dell'Insubria, 2016).

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