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.