Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning

Yu Jung Tsai; Alexandre Bousse; Matthias J. Ehrhardt; Charles W. Stearns; Sangtae Ahn; Brian F. Hutton; Simon Arridge; Kris Thielemans

doi:10.1109/TMI.2017.2786865

Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning

Yu Jung Tsai
, Alexandre Bousse
, Matthias J. Ehrhardt
, Charles W. Stearns
, Sangtae Ahn
, Brian F. Hutton
, Simon Arridge
, Kris Thielemans

Institute for Mathematical Innovation (IMI)

University College London
University of Cambridge
GE Healthcare, United States
GE Global Research NY
University of Wollongong

Research output: Contribution to journal › Article › peer-review

21 Citations (SciVal)

Abstract

This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three ¹⁸F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

Original language	English
Pages (from-to)	1000-1010
Number of pages	11
Journal	IEEE Transactions on Medical Imaging
Volume	37
Issue number	4
Early online date	25 Dec 2017
DOIs	https://doi.org/10.1109/TMI.2017.2786865
Publication status	Published - 1 Apr 2018

Funding

Manuscript received September 25, 2017; revised December 11, 2017; accepted December 18, 2017. Date of publication December 25, 2017; date of current version April 2, 2018. This work was supported in part by GE Healthcare and in part by the NIHR-funded UCLH Biomedical Research Centre. The work of M. J. Ehrhardt was supported in part by the Leverhulme Trust Project—Breaking the non-convexity barrier, EPSRC, under Grant EP/M00483X/1 and Grant EP/N014588/1, in part by the Cantab Capital Institute for the Mathematics of Information, and in part by CHiPS (Horizon 2020 RISE Project Grant). (Corresponding author: Yu-Jung Tsai.) Y.-J. Tsai, A. Bousse, and K. Thielemans are with the Institute of Nuclear Medicine, University College London, London NW1 2BU, U.K. (e-mail: [email protected]).

Keywords

Emission tomography
L-BFGS-B
penalized reconstruction
preconditioning

ASJC Scopus subject areas

Software
Radiological and Ultrasound Technology
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TMI.2017.2786865Licence: CC BY

Cite this

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title = "Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning",

abstract = "This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.",

keywords = "Emission tomography, L-BFGS-B, penalized reconstruction, preconditioning",

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AU - Tsai, Yu Jung

AU - Bousse, Alexandre

AU - Ehrhardt, Matthias J.

AU - Stearns, Charles W.

AU - Ahn, Sangtae

AU - Hutton, Brian F.

AU - Arridge, Simon

AU - Thielemans, Kris

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N2 - This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

AB - This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

KW - Emission tomography

KW - L-BFGS-B

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KW - preconditioning

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Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning

Abstract

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Keywords

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