 
Summary: 4 th World Congress on Industrial Process Tomography, Aizu, Japan
Full shape reconstruction from partial ERT monotonicity information
using a BayesMCMC approach
Robert G Aykroyd 1 , Manuchehr Soleimani 2 and William RB Lionheart 2
1 Department of Statistics, University of Leeds, Leeds, LS2 9JT, UK, robert@maths.leeds.ac.uk,
2 Department of Mathematic, University of Manchester, Manchester, M60 1QD, UK
ABSTRACT
Many applications of tomography seek to image twophase materials, such as oil and air, with the idealized
aim of producing a binary reconstruction. The method of Tamburrino et al. (2002) provides a noniterative
approach, which requires modest computational effort, and hence appears to achieve this aim. Specifically, it
requires the solution of a number of forward problems increasing only linearly with the number of elements
used to discretize the unknown domain. However, even for errorfree data the method only gives a definitive
classification for a part of the image. For examples when even low measurement noise is present relatively
few domain elements can be classified and hence only a partial reconstruction is possible. This paper looks
at the use of a Bayesian approach based on the monotonicity information for reconstructing the shape of a
homogeneous resistivity inclusion in another homogeneous resistivity material. In particular, the monotonicity
criterion is used to fix the resistivity of some elements. The uncertain element resistivities are then estimated,
conditional upon the fixed values. In addition, other summary output is presented such as marginal posterior
distributions, and confidence intervals. The methods will be illustrated using simulation examples covering a
range of object geometries, sensor numbers and noise levels.
