Open Access Open Access  Restricted Access Subscription or Fee Access

Detection of multiple rigid inclusions from ERT data using the complete-electrode model

Taysir E. Dyhoum, Robert G. Aykroyd, Daniel Lesnic


This paper considers inverse shape reconstruction of rigid inclusions from electrical resistance tomography data and presents a novel combination of forward solution using the method of fundamental solutions (MFS) and Bayesian inverse reconstruction through a Markov chain Monte Carlo (MCMC) algorithm. The MFS provides fast and highly accurate forward solution with less computational effort than the more standard boundary element
and finite element methods. This is particularly important as MCMC inverse solution requires the forward problem to be solved thousands of times. However, using the Bayesian approach and MCMC estimation has big advantages in terms of uncertainty and reliability assessment. The mathematical model is governed by the two-dimensional Laplace’s equation in a multiply-connected domain subject to a homogeneous Dirichlet boundary condition on the unknown rigid inclusion and a piecewise Robin boundary condition on the outer boundary containing the electrodes. The measurements are the constant voltage values on the electrodes calculated from multiple current patterns and solving the inverse problem means detecting the location, shape and size of the inner object, as well as the contact impedances for each electrode (if unknown). A series of numerical examples using
simulated data demonstrate the accuracy and stability of the proposed approach.


Bayesian methods, complete-electrode model, contact impedance, electrical resistance tomography, method of fundamental solutions, Markov chain Monte Carlo.

Full Text:


Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information. Also: DOI is paid service which provided by a third party. We never mentioned that we go for this for our any journal. However, journal have no objection if author go directly for this paid DOI service.