Analysis of Anisotropic Inverse Boundary Value Problems

Lead Research Organisation: University of Manchester
Department Name: Mathematics


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.


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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