Spatially-Adaptive Variational Reconstructions for Linear Inverse Electrical Impedance Tomography

The inverse electrical impedance tomography (EIT) problem involves collecting electrical measurements on the smooth boundary of a region to determine the spatially varying electrical conductivity distribution within the bounded region. Effective applications of EIT technology emerged in different areas of engineering, technology, and applied sciences. However, the mathematical formulation of EIT is well known to suffer from a high degree of nonlinearity and severe ill-posedness. Therefore, regularization is required to produce reasonable electrical impedance images. Using difference imaging, we propose a spatially-variant variational method which couples sparsity regularization and smoothness regularization for improved EIT linear reconstructions. The EIT variational model can benefit from structural prior information in the form of an edge detection map coming either from an auxiliary image of the same object being reconstructed or automatically detected. We propose an efficient algorithm for minimizing the (non-convex) function based on the alternating direction method of multipliers. Experiments are presented which strongly indicate that using non-convex versus convex variational EIT models holds the potential for more accurate reconstructions.