Regularization methods for the solution of a nonlinear least-squares problem in tomography

Bernardini, Stefano (2015) Regularization methods for the solution of a nonlinear least-squares problem in tomography. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Bernardini, Stefano
Relatore della tesi
Correlatore della tesi
Corso di studio
Curriculum A: Generale e applicativo
Ordinamento Cds
Parole chiave
image reconstruction tomography nonlinear least-squares problem polyenergetic multimaterial model regularization methods
Data di discussione della Tesi
17 Luglio 2015

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