A Combined Wavelet-Based Mesh-Free Method for Solving the Forward Problem in Electrical Impedance Tomography

In this paper, a combined wavelet-based mesh-free method is suggested to solve the forward problem in electrical impedance tomography (EIT). EIT is a noninvasive imaging modality based on the reconstruction of the conductivity profile inside a solution domain. The forward problem simulates measurement data for comparing with experimental data in the inverse problem. The forward problem can be solved by the finite element method (FEM) or the mesh-free method. Since the solution of the FEM depends on the mesh shape and boundary condition constraints are difficult to be applied to the mesh-free method, the combined wavelet-based mesh-free approach can resolve the disadvantages of both methods in the EIT forward problem. In order to apply interface conditions between different regions, slope jump functions are entered to the set of basis functions. Two different 2-D EIT problems are modeled. The simulation results obtained by the combined wavelet-based mesh-free method are compared with the FEM in terms of accuracy and computational cost. Moreover, the effects of object movement and deformation are investigated on the accuracy of the simulated electrode voltages using the standard FEM and combined wavelet-based mesh-free method.