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Under-relaxed quasi-Newton acceleration for an inverse fixed-point problem coming from Positron Emission Tomography

  • Tiara Martini dos Santos ORCID logo EMAIL logo , Louise Reips and José Mario Martínez
Published/Copyright: March 29, 2018

Abstract

Quasi-Newton acceleration is an interesting tool to improve the performance of numerical methods based on the fixed-point paradigm. In this paper, a briefly description of the compartmental model employed for a typical task in perfusion imaging is presented. Next, a quasi-Newton strategy for accelerating the convergence of fixed-point iterations is analyzed. For that, classical secant updates are considered. Finally, the quasi-Newton strategy is applied on the practical problem of represent the kinetic behavior of a PET (Positron Emission Tomography) tracer during cardiac perfusion. The performance of the method when applied to real data problems is illustrated numerically.

Award Identifier / Grant number: 2012/10444-0

Funding statement: The authors acknowledge the support for the present research provided by FAPESP, under Research Grant No. 2012/10444-0.

Acknowledgements

We should like to thank Professor Martin Burger (Institute for Computational and Applied Mathematics University of Münster) for useful suggestions about this paper. In addition, the authors would like to thank the anonymous referees for their carefully reading of the manuscript and for several constructive comments that improve the presentation of this work.

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Received: 2016-09-14
Revised: 2017-10-24
Accepted: 2018-03-13
Published Online: 2018-03-29
Published in Print: 2018-12-01

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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