Cao, K and Lesnic, D (2018) Reconstruction of the perfusion coefficient from temperature measurements using the conjugate gradient method. International Journal of Computer Mathematics, 95 (4). pp. 797-814. ISSN 0020-7160
Abstract
We consider the inverse bio-heat transfer problem to determine the space- and time-dependent perfusion coefficient from temperature measurements. In this formulation, the problem is fully determined and the coefficient is identifiable if and only if the temperature has dense support. However, the problem is still ill-posed since small errors in the measured temperature cause large errors in the output perfusion coefficient due to the numerical differentiation of noisy data involved which represents an unstable procedure. In order to overcome this difficulty and restore stability, we employ for the first time the conjugate gradient method (CGM) for solving the inverse problem under investigation. Regularization is achieved by stopping the iteration process at an appropriate threshold dictated by the discrepancy principle. Numerical results show that the CGM is accurate and reasonably stable in retrieving the perfusion coefficient. Moreover, comparison with other methods shows improved efficiency and stability in inverting noisy data.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Computer Mathematics on the 13th March, 2017, available online: http://www.tandfonline.com/10.1080/00207160.2017.1296955 |
Keywords: | Inverse problem, bio-heat equation, ill-posed problem, conjugate gradient method, perfusion coefficient |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Feb 2017 11:38 |
Last Modified: | 19 Mar 2018 16:21 |
Status: | Published |
Publisher: | Taylor & Francis |
Identification Number: | 10.1080/00207160.2017.1296955 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:112412 |