Analysis of Anisotropic Inverse Boundary Value Problems

Lead Research Organisation: University of Manchester
Department Name: Mathematics

Abstract

Effects of anisotropy are important in electrical, acoustical and optical imaging used in non-destructive testing, geophysics and medical imaging. If ignored these effects can result in a wrong solution to the inverse problem. There are currently very few theoretical results on scalar anisotropic inverse problems with no general approach towards stability and development of convergent reconstruction algorithms for solving these problems. Almost nothing is known about inverse boundary value problems for systems of partial differential equations, especially in the anisotropic case. The aim of this research is to develop analytical and geometric methods to study uniqueness and stability in anisotropic inverse problems and to implement these methods by developing convergent reconstruction algorithms for solving fully non-linear inverse boundary value problems.

Publications

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Abascal J (2011) Electrical impedance tomography in anisotropic media with known eigenvectors in Inverse Problems

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Adler A (2010) Correcting for variability in mesh geometry in finite element models in Journal of Physics: Conference Series

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Doeva O (2020) Lipschitz stability at the boundary for time-harmonic diffuse optical tomography in Applicable Analysis

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Doeva O (2020) Lipschitz stability at the boundary for time-harmonic diffuse optical tomography

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Gaburro R (2009) Recovering Riemannian metrics in monotone families from boundary data in Inverse Problems

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Grychtol B (2012) Impact of model shape mismatch on reconstruction quality in electrical impedance tomography. in IEEE transactions on medical imaging

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Liu W (2012) The free radical species in polyacrylonitrile fibers induced by ?-radiation and their decay behaviors in Radiation Physics and Chemistry

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Paridis K (2010) Shape corrections for 3D EIT in Journal of Physics: Conference Series

 
Description We found consistency conditions and uniqueness results for discrete versions of the anisotropic inverse conductivity problem that is useful in medical imaging. We also found uniqueness results and reconstruction algorithms for other anisotropic electromagnetic problems useful for example in measuring strain with polarized light
Exploitation Route The work in this proposal continues to be used in our work on electrical impedance tomography for medical imaging and in tomographic imaging of tensor fields in materials science and engineering
Sectors Aerospace, Defence and Marine,Healthcare,Manufacturing, including Industrial Biotechology
 
Description The work in the programme contributed to future work especially by Kurylev, on electromagnetic cloaking, and geometric inverse problems taht could be applied to elstographic tomography in medical imaging
First Year Of Impact 2016
Sector Aerospace, Defence and Marine,Electronics,Healthcare
 
Description EPSRC
Amount £498,383 (GBP)
Funding ID EP/K00428X/1 
Organisation Engineering and Physical Sciences Research Council (EPSRC) 
Sector Public
Country United Kingdom
Start 04/2012 
End 03/2013