An unfortunate occurrence in experimental measurements with electrical impedance tomography is electrodes which become detached or poorly connected, such that the measured data cannot be used. This paper develops an image reconstruction methodology which allows use of the remaining valid data. A finite element model of the EIT difference imaging forward problem is linearized as z = Hx, where z represents the change in measurements and x the element log conductivity changes. Image reconstruction is represented in terms of a maximum a posteriori (MAP) estimate as x = inv(Htinv(Rn) + inv(Rx))Htinv(Rn)z, where Rx and Rn represent the a priori estimates of image and measurement noise crosscorrelations, respectively. Using this formulation, missing electrode data can be naturally modelled as infinite noise on all measurements using the affected electrodes. Simulations indicate position error and resolution are close (+/- 10%) to the values calculated without missing electrode data as long as the target was further than 10% of the medium diameter from the affected electrode. Applications of this technique to experimental data show good results in terms of removing artefacts from images.