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.
Organisations
People |
ORCID iD |
William Lionheart (Principal Investigator) |
Publications
Abascal J
(2011)
Electrical impedance tomography in anisotropic media with known eigenvectors
in Inverse Problems
Adler A
(2010)
Correcting for variability in mesh geometry in finite element models
in Journal of Physics: Conference Series
Doeva O
(2020)
Lipschitz stability at the boundary for time-harmonic diffuse optical tomography
in Applicable Analysis
Gaburro R
(2009)
Recovering Riemannian metrics in monotone families from boundary data
in Inverse Problems
Grychtol B
(2012)
Impact of Model Shape Mismatch on Reconstruction Quality in Electrical Impedance Tomography
in IEEE Transactions on Medical Imaging
Liu W
(2012)
The free radical species in polyacrylonitrile fibers induced by ?-radiation and their decay behaviors
in Radiation Physics and Chemistry
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 | 03/2012 |
End | 03/2013 |