Stability analysis in magnetic resonance elastography II

Heiko Gimperlein, Alden Waters

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Abstract

We consider the inverse problem of finding unknown elastic parameters from internal measurements of displacement fields for tissues. In the sequel to Ammari, Waters, Zhang (2015), 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.
Original languageEnglish
Pages (from-to)1801-1812
Number of pages12
JournalJournal of Mathematical Analysis and Applications
Volume434
Issue number2
Early online date13 Oct 2015
DOIs
Publication statusPublished - 15 Feb 2016

Keywords

  • Stability analysis
  • Shear modulus reconstruction
  • Magnetic resonance elastography
  • Landweber scheme
  • Biological tissues
  • Optimal control

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