Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm

Emil Y. Sidky; Per Christian Hansen; Jakob S. Jørgensen; Xiaochuan Pan

doi:10.1117/12.2646511

Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm

Emil Y. Sidky, Per Christian Hansen, Jakob S. Jørgensen, Xiaochuan Pan

The University of Chicago

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

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Abstract

The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.

Original language	English
Title of host publication	Proceedings of the 7th International Conference on Image Formation in X-Ray Computed Tomography
Number of pages	7
Volume	12304
Publisher	SPIE
Publication date	2022
Article number	1230406
ISBN (Print)	9781510656697
ISBN (Electronic)	9781510656703
DOIs	https://doi.org/10.1117/12.2646511
Publication status	Published - 2022
Event	7th International Conference on Image Formation in X-Ray Computed Tomography - Baltimore, United States Duration: 12 Jun 2022 → 16 Jun 2022 Conference number: 7

Conference

Conference	7th International Conference on Image Formation in X-Ray Computed Tomography
Number	7
Country/Territory	United States
City	Baltimore
Period	12/06/2022 → 16/06/2022

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@inproceedings{62c4b8d2404c4da4963257606a6859fe,

title = "Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm",

abstract = "The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.",

author = "Sidky, {Emil Y.} and Hansen, {Per Christian} and J{\o}rgensen, {Jakob S.} and Xiaochuan Pan",

note = "Publisher Copyright: {\textcopyright} 2022 SPIE.; 7th International Conference on Image Formation in X-Ray Computed Tomography ; Conference date: 12-06-2022 Through 16-06-2022",

year = "2022",

doi = "10.1117/12.2646511",

language = "English",

isbn = "9781510656697",

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booktitle = "Proceedings of the 7th International Conference on Image Formation in X-Ray Computed Tomography",

publisher = "SPIE",

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Sidky, EY, Hansen, PC , Jørgensen, JS & Pan, X 2022, Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm. in Proceedings of the 7th International Conference on Image Formation in X-Ray Computed Tomography. vol. 12304, 1230406, SPIE, 7th International Conference on Image Formation in X-Ray Computed Tomography, Baltimore, Maryland, United States, 12/06/2022. https://doi.org/10.1117/12.2646511

Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm. / Sidky, Emil Y.; Hansen, Per Christian ; Jørgensen, Jakob S. et al.
Proceedings of the 7th International Conference on Image Formation in X-Ray Computed Tomography. Vol. 12304 SPIE, 2022. 1230406.

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

TY - GEN

T1 - Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm

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AU - Hansen, Per Christian

AU - Jørgensen, Jakob S.

AU - Pan, Xiaochuan

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N2 - The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.

AB - The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application to CT when using unmatched back-projector/projector pairs and when applying preconditioning. The GMRES algorithm is demonstrated on a 3D CT image reconstruction problem where it is seen that use of unmatched projection matrices does not prevent convergence, while using an unmatched pair in the related conjugate gradients for least-squares (CGLS) algorithm leads to divergent iteration. Implementation of preconditioning using GMRES is also demonstrated.

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DO - 10.1117/12.2646511

M3 - Article in proceedings

AN - SCOPUS:85129749538

SN - 9781510656697

VL - 12304

BT - Proceedings of the 7th International Conference on Image Formation in X-Ray Computed Tomography

PB - SPIE

T2 - 7th International Conference on Image Formation in X-Ray Computed Tomography

Y2 - 12 June 2022 through 16 June 2022

ER -

Iterative image reconstruction for CT with unmatched projection matrices using the generalized minimal residual algorithm

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