Reconstructing Electrical Impedance Tomography 3D Brain Images with Anatomical Atlas and Total Variation Priors

Electrical Impedance Tomography (EIT) is an imaging modality that allows the visualization of internal resistivities of a region of interest from electrical measurements external to the same region. In this work, we reconstruct 3D static images using two regularization terms, an anatomical atlas with \(\ell _1\) -norm and a total variation (TV) term. We chose the iteratively reweighted least squares (IRLS) algorithm to approximate the \(\ell _1\) -norms by quadratic terms and the Gauss-Newton algorithm to perform the optimization of the resulting functional. Together with the anatomical atlas, using a traditional \(\ell _2\) -norm and a high-pass filter as the regularizer tends to reconstruct the target on the mesh elements near the region boundary. In comparison, the reconstructed targets with the proposed method are better located, especially when reconstructing multiple targets, in addition to detecting a higher resistivity variation with the same number of iterations.