Email: robert6@mdx.ac.uk

CompanyName: Middlesex University

Country: UK

Abstract: Feasibility of EIT image reconstruction via combinatorial optimisation

R.D. Ettinger (*), S.H. Khan (**) and B.M.A. Rahman (**)

* School of Computing Science, Middlesex
University, London, UK

** School of Engineering, City University, London, UK

The reconstruction of images from EIT boundary data may involve solving the
forward problem on a finite element mesh that covers the entire inhomogeneous
region to be imaged. Alternatively there are boundary element approaches that
require the whole region to be segmented into separate organs that have homogeneous
electrical properties. Following discretisation by either method, the inverse
problem can be attacked.

Our talk will propose a new starting point where the solution space for solving the inverse problem is a finite set of simple conductivity patterns. Every such pattern has identical homogeneous background material of complex permittivity p1, with a number of very small homogeneous discs (or spheres in the 3D problem) of permittivity p2 at specified locations.

These “dot patterns” are distinguished purely via their unique sets of disk (or sphere) locations.

Finite element or boundary element techniques are not required for solving the “dot pattern” forward problem if a suitable approximate formula for the effect of “dots” on EIT boundary data is employed. A linear formula can be used if the dots are assumed to act like uncoupled dipoles, in which case the effect of any dot pattern is very cheap to calculate. We will describe, for this case, a search algorithm that converges to a pattern offering local best fit with the measured boundary data. (There is no reason to pre-compute the forward solutions since the number of patterns visited will only be a tiny subset of a much larger combinatorial space).

Numerical examples will be given to show how the approach produces approximate dot images related to some simple phantoms that are not themselves in the assumed solution space. A way to convert a discrete dot pattern back to a conventional image will be discussed.

We will discuss the relevance of this work to real-time medical EIT. Obvious limitations and future plans will be explained.