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The research plan aims to study new techniques for the solution of linear inverse problems with particular attention to the ones arising from signal processing and image restoration. After suitable discretization, such problems typically lead to (severely) ill-conditioned linear systems of equations, which require to be regularized in some way, in order to compute a meaningful approximation of the solution.
In this framework we are mainly interested in iterative methods of Krylov type based on the Arnoldi or Lanczos algorithm, in connection with the Tikhonov regularization approach. We plan to study new strategies for the construction of the regularization operator and for the definition of the continuous and the discrete regularization parameters. A possible use of extrapolation techniques will also be considered.
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