Weighted regularization in electrical impedance tomography with applications to acute cerebral stroke

We apply electrical impedance tomography to detect and localize brain impedance changes associated with stroke. Forward solutions are computed using the finite-element method in two dimensions. We assume that baseline conductivity values are known for the major head tissues, and focus on changes in the brain compartment only. We use singular-value decomposition (SVD) to show that different impedance measurement patterns, which are theoretically equivalent by the reciprocity theorem, have different sensitivities to the brain compartment in the presence of measurement noise. The inverse problem is solved in part by standard means, using iterated SVD, and regularizing by truncation. To improve regularization we introduce a weighting scheme which normalizes the sensitivity matrix for voxels at different depths. This increases the number of linearly independent components which contribute to the solution, and forces the different measurement patterns to have similar sensitivity. When applied to stroke, this weighted regularization improves image quality overall.