We study strategies to increase the precision in deconvolution models, while maintaining the complexity of the related numerical linear algebra procedures (matrix-vector product, linear system solution, computation of eigenvalues, etc.) of the same order of the celebrated fast Fourier transform. The key idea is the choice of a suitable functional basis to represent signals and images. Starting from an analysis of the spectral decomposition of blurring matrices associated to the antireflective boundary conditions introduced in Serra Capizzano (SIAM J. Sci. Comput. 25(3):1307–1325, 2003), we extend the model for preserving polynomials of higher degree and fast computations also in the nonsymmetric case. We apply the proposed model to Tikhonov regularization with smoothing norms and the generalized cross validation in order to choose the regularization parameter. A selection of numerical experiments shows the effectiveness of the proposed techniques.

Fast transforms for high order boundary conditions in deconvolution problems

DONATELLI, MARCO
2010-01-01

Abstract

We study strategies to increase the precision in deconvolution models, while maintaining the complexity of the related numerical linear algebra procedures (matrix-vector product, linear system solution, computation of eigenvalues, etc.) of the same order of the celebrated fast Fourier transform. The key idea is the choice of a suitable functional basis to represent signals and images. Starting from an analysis of the spectral decomposition of blurring matrices associated to the antireflective boundary conditions introduced in Serra Capizzano (SIAM J. Sci. Comput. 25(3):1307–1325, 2003), we extend the model for preserving polynomials of higher degree and fast computations also in the nonsymmetric case. We apply the proposed model to Tikhonov regularization with smoothing norms and the generalized cross validation in order to choose the regularization parameter. A selection of numerical experiments shows the effectiveness of the proposed techniques.
2010
BIT
http://link.springer.com/article/10.1007/s10543-010-0266-4
Donatelli, Marco
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/11383/1717855
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? 14
social impact