Improving the Computational Cost of Image Reconstruction in Biomedical Magnetic Induction Tomography Using a Volume Integral Equation Approach

Magnetic induction tomography is a novel imaging method with promising biomedical applications. The image reconstruction problem suffers from a high computation cost because of its inherent nonlinearity. Current state-of-the-art numerical methods are based on the finite element method (FEM). To avoid artifacts at the boundaries, this method requires the discretization of a volume much larger than the actual volume of interest. A numerical model based on volume integrals only requires the discretization of the volume of interest, which greatly reduces the number of unknowns. Fewer unknowns generally imply a lower computation cost. However, a naive implementation of the volume integral equation does not yield a lower computation cost due to the bad conditioning arising from the high dielectric property values of biological tissues at low frequencies. To tackle this problem, a model based on inhomogeneous Green's function is proposed. The forward model is validated with the Mie scattering theory. Through the resolution of the inverse problem, it is found that the reconstruction limits compare well with current state-of-the-art methods. By reducing the number of unknowns and maintaining a similar computational complexity, the proposed model offers a computation cost reduction when compared with the FEM.