Stability analysis in magnetic resonance elastography II

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:434

Article

Gimperlein, Heiko^1,2,3  Waters, Alden⁴ 

[1] Heriot Watt Univ, Maxwell Inst Math Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland

[3] Univ Paderborn, Inst Math, Warburger St 100, D-33098 Paderborn, Germany

[4] UCL, Dept Math, Gower St, London WC1E 6BT, England

关键词: Stability analysis;    Shear modulus reconstruction;    Magnetic resonance elastography;    Landweber scheme;    Biological tissues;    Optimal control;   

DOI  :  10.1016/j.jmaa.2015.10.010

来源: Elsevier

【 摘 要 】

We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. In the sequel to [5], we use pseudodifferential methods for the problem of recovering the shear modulus for Stokes systems from internal data. We prove stability estimates in d = 2,3 with reduced regularity on the estimates and show that the presence of a finite dimensional kernel can be removed. This implies the convergence of the Landweber numerical iteration scheme. We also show that these hypotheses are natural for experimental use in constructing shear modulus distributions. (C) 2015 Published by Elsevier Inc.

【 授权许可】

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