Author
Adler A.
Institution
Sch. of Inf. Technol. & Eng., Ottawa Univ., Ont., Canada.
Title
Accounting for missing electrode data in electrical impedance tomography
Source
Conference Information
4th Conference on Biomedical Applications of Electrical Impedance
Tomography
UMIST, Manchester April 23-25 2003.
Abstract
An unfortunate, but not unusual, occurrence in experimental
measurements with Electrical Impedance Tomography, is electrodes
which become detached or poorly connected, such that the measured
data cannot be used. We propose an image reconstruction methodology
which allows use of the remaining good measurements. A finite element
model of the EIT dynamic imaging forward problem is linearized
as z=Hx, where z is the vector change in measurements and x the
vector of change in finite element log conductivities. Image
reconstruction is represented in terms of a Maximum a Posteriori
(MAP) estimate as x=inv(H'*inv(Rn)*H + inv(Rx))*H'*inv(Rn)*z, where
(') represents the transpose operator, and Rx and Rn represent the a
priori estimates of image and measurement noise cross correlations,
respectively. Using this formulation, missing electrode data can be
naturally modelled as infinite noise on all measurements using the
corresponding electrodes. Simulations were conducted of a small
contrasting target at different radial positions as a function
of the position of the problem electrode. Contrast position error,
point spread function, and total image amplitude were calculated. All
values are close (±10%) to those calculated without missing electrode
data as long as the target was further from the problem electrode
than 10% of the medium diameter. When the target was closer
than this limit, all error values increased significantly, but
the reconstructed image still represented a reasonable "best
effort". Application of this technique to experimental data shows
similar results. In comparison, simulations were made of the
simple approach of setting measurements from problem electrodes
to zero. Results show significant errors for targets 25% of the
medium diameter from the electrode. The increase in point spread
function size above the value for no electrode errors was three
times greater for this simple approach than for the MAP estimate.