We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilai-Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations.

Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

LOLI PICCOLOMINI, Elena
Primo
Membro del Collaboration Group
;
Coli Vl
Secondo
Membro del Collaboration Group
;
Zanni L.
Ultimo
Membro del Collaboration Group
2018

Abstract

We propose a scaled gradient projection algorithm for the reconstruction of 3D X-ray tomographic images from limited data. The problem arises from the discretization of an ill-posed integral problem and, due to the incompleteness of the data, has infinite possible solutions. Hence, by following a regularization approach, we formulate the reconstruction problem as the nonnegatively constrained minimization of an objective function given by the sum of a fit-to-data term and a smoothed differentiable Total Variation function. The problem is challenging for its very large size and because a good reconstruction is required in a very short time. For these reasons, we propose to use a gradient projection method, accelerated by exploiting a scaling strategy for defining gradient-based descent directions and generalized Barzilai-Borwein rules for the choice of the step-lengths. The numerical results on a 3D phantom are very promising since they show the ability of the scaling strategy to accelerate the convergence in the first iterations.
2018
LOLI PICCOLOMINI, Elena; Coli, Vl; Morotti, E; Zanni, L.
File in questo prodotto:
File Dimensione Formato  
paper_rev_mo_20170918.pdf

accesso aperto

Descrizione: Post-print
Tipologia: Post-print
Licenza: PUBBLICO - Pubblico con Copyright
Dimensione 2.62 MB
Formato Adobe PDF
2.62 MB Adobe PDF Visualizza/Apri
Piccolomini2018_Article_ReconstructionOf3DX-rayCTImage.pdf

solo gestori archivio

Descrizione: Full text editoriale
Tipologia: Full text (versione editoriale)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 3.09 MB
Formato Adobe PDF
3.09 MB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in SFERA 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/11392/2377726
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 11
  • ???jsp.display-item.citation.isi??? 11
social impact