We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state of the art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional preconditioning.

Fast nonstationary preconditioned iterative methods for ill-posed problems, with application to image deblurring

DONATELLI, MARCO;
2013-01-01

Abstract

We introduce a new iterative scheme for solving linear ill-posed problems, similar to nonstationary iterated Tikhonov regularization, but with an approximation of the underlying operator to be used for the Tikhonov equations. For image deblurring problems such an approximation can be a discrete deconvolution that operates entirely in the Fourier domain. We provide a theoretical analysis of the new scheme, using regularization parameters that are chosen by a certain adaptive strategy. The numerical performance of this method turns out to be superior to state of the art iterative methods, including the conjugate gradient iteration for the normal equation, with and without additional preconditioning.
2013
Donatelli, Marco; Hanke, M.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1831519
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 34
  • ???jsp.display-item.citation.isi??? 32
social impact