  This work considers the optimization of electrode positions in head imaging
by electrical impedance tomography. The study is motivated by maximizing the
sensitivity of electrode measurements to conductivity changes when monitoring
the condition of a stroke patient, which justifies adopting a linearized
version of the complete electrode model as the forward model. The algorithm is
based on finding a (locally) A-optimal measurement configuration via gradient
descent with respect to the electrode positions. The efficient computation of
the needed derivatives of the complete electrode model is one of the focal
points. Two algorithms are introduced and numerically tested on a three-layer
head model. The first one assumes a region of interest and a Gaussian prior for
the conductivity in the brain, and it can be run offline, i.e., prior to taking
any measurements. The second algorithm first computes a reconstruction of the
conductivity anomaly caused by the stroke with an initial electrode
configuration by combining lagged diffusivity iteration with sequential
linearizations, which can be interpreted to produce an approximate Gaussian
probability density for the conductivity perturbation. It then resorts to the
first algorithm to find new, more informative positions for the available
electrodes with the constructed density as the prior.
