An Automatic Neural-Networks Based Mesh Refinement Method for Electrical Impedance Tomography

In real life applications, inverse problems, such as the electrical impedance tomography problem, usually have a limited accuracy, and require huge computation resources to be solved correctly. In electrical impedance tomography, the goal is to obtain the electrical properties of different materials (typically living tissues) by applying an electrical current and measuring the resulting potential difference at the boundaries of the domain. While the maximum numerical accuracy is technically limited by the size of the elements within the finite element mesh, using a fine mesh will result in a computationally demanding reconstruction, especially when the location of the target is unknown. However, this situation is different when the location of the target is known in advance. In this case, one can easily refine the finite element model around the target, allowing a greater accuracy around the region of interest. In this paper, a novel approach estimates the location of the target object before solving the inverse problem, so that it becomes possible to refine only a specific area of the element domain. An artificial neural network is used to determine the location of the target directly from voltages measured at the boundary of the domain. This location is then used to refine the mesh at this specific location, which increases the accuracy without significantly affect the computation resources necessary to solve the inverse problem. Since linear inverse solvers give a linear conductivity distribution, it was decided to use the h-method to refine the mesh around the target object.