Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography

Per Christian Hansen; Jakob Sauer Jørgensen; Peter Winkel Rasmussen

doi:10.1109/ICCSA54496.2021.00019

Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography

Per Christian Hansen, Jakob Sauer Jørgensen, Peter Winkel Rasmussen

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

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Abstract

Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.

Original language	English
Title of host publication	Proceedings of 21^st International Conference on Computational Science and Its Applications (ICCSA)
Publisher	IEEE
Publication date	2022
Pages	60-70
Article number	9732394
ISBN (Print)	978-1-6654-5844-3
DOIs	https://doi.org/10.1109/ICCSA54496.2021.00019
Publication status	Published - 2022
Event	21^st International Conference on Computational Science and Its Applications - University of Cagliari, Cagliari, Italy Duration: 13 Sept 2021 → 16 Sept 2021 Conference number: 21 https://2021.iccsa.org/

Conference

Conference	21^st International Conference on Computational Science and Its Applications
Number	21
Location	University of Cagliari
Country/Territory	Italy
City	Cagliari
Period	13/09/2021 → 16/09/2021
Internet address	https://2021.iccsa.org/

Keywords

Tomographic reconstruction
Iterative methods
Stopping rules
Semi-convergence

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10.1109/ICCSA54496.2021.00019

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title = "Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography",

abstract = "Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.",

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author = "Hansen, {Per Christian} and J{\o}rgensen, {Jakob Sauer} and Rasmussen, {Peter Winkel}",

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booktitle = "Proceedings of 21st International Conference on Computational Science and Its Applications (ICCSA)",

publisher = "IEEE",

address = "United States",

note = "21<sup>st</sup> International Conference on Computational Science and Its Applications, ICCSA 2021 ; Conference date: 13-09-2021 Through 16-09-2021",

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Hansen, PC , Jørgensen, JS & Rasmussen, PW 2022, Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography. in Proceedings of 21^st International Conference on Computational Science and Its Applications (ICCSA)., 9732394, IEEE, pp. 60-70, 21^st International Conference on Computational Science and Its Applications, Cagliari, Italy, 13/09/2021. https://doi.org/10.1109/ICCSA54496.2021.00019

Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography. / Hansen, Per Christian ; Jørgensen, Jakob Sauer ; Rasmussen, Peter Winkel.
Proceedings of 21^st International Conference on Computational Science and Its Applications (ICCSA). IEEE, 2022. p. 60-70 9732394.

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

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N2 - Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.

AB - Algebraic models for the reconstruction problem in X-ray computed tomography (CT) provide a flexible framework that applies to many measurement geometries. For large-scale problems we need to use iterative solvers, and we need stopping rules for these methods that terminate the iterations when we have computed a satisfactory reconstruction that balances the reconstruction error and the influence of noise from the measurements. Many such stopping rules are developed in the inverse problems communities, but they have not attained much attention in the CT world. The goal of this paper is to describe and illustrate four stopping rules that are relevant for CT reconstructions.

KW - Tomographic reconstruction

KW - Iterative methods

KW - Stopping rules

KW - Semi-convergence

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BT - Proceedings of 21st International Conference on Computational Science and Its Applications (ICCSA)

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T2 - 21<sup>st</sup> International Conference on Computational Science and Its Applications

Y2 - 13 September 2021 through 16 September 2021

ER -

Stopping Rules for Algebraic Iterative Reconstruction Methods in Computed Tomography

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Keywords

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