Conditional-Bayes reconstruction for ERT data using resistance monotonicity information

Robert G. Aykroyd, Manuchehr Soleimani, & William R.B. Lionheart

Many applications of tomography seek to image two-phase materials, such as oil and air, with the idealized aim of producing a binary reconstruction. The method of Tamburrino et al. (2002) provides a non-iterative approach, which requires modest computational e ort, 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 represent the domain where the resistivity is unknown. However, even when low measurement noise is present it may be that not all 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 pixels. The uncertain pixel resistivities are then estimated, conditional upon the fixed values. This has the e ect of both producing better reconstructions, but also reducing the computational burden by up to an order of magnitude in the examples considered. The methods are illustrated using simulation examples covering a range of object geometries.

Keywords: Bayesian statistics; Electrical tomography; Markov Chain ; Monte Carlo; Posterior estimation.