Reconstruction of electrical impedance tomography (EIT) images based on the expectation maximum (EM) method

Electrical impedance tomography (EIT) calculates the internal conductivity distribution within a body using electrical contact measurements. The image reconstruction for EIT is an inverse problem, which is both non-linear and ill-posed. The traditional regularization method cannot avoid introducing negative values in the solution. The negativity of the solution produces artifacts in reconstructed images in presence of noise. A statistical method, namely, the expectation maximization (EM) method, is used to solve the inverse problem for EIT in this paper. The mathematical model of EIT is transformed to the non-negatively constrained likelihood minimization problem. The solution is obtained by the gradient projection-reduced Newton (GPRN) iteration method. This paper also discusses the strategies of choosing parameters. Simulation and experimental results indicate that the reconstructed images with higher quality can be obtained by the EM method, compared with the traditional Tikhonov and conjugate gradient (CG) methods, even with non-negative processing. ► The expectation maximization method is used to solve the inverse problem for EIT. ► The mathematical model of EIT is transformed to likelihood minimization problem. ► The noise level of the measurement system is considered as prior information. ► The EM method can obtain a non-negative solution and low image distortion. ► The EM method is robust to measurement noise.