A Permittivity Imaging Method by Sensitivity Matrix Gradient: Electrical Capacitance Tomography Based on Electromagnetic Momentum

Electrical capacitance tomography (ECT) is a commonly used permittivity imaging method in industrial inspection. The nonlinear relationship between capacitance and permittivity, as well as the inverse problem being ill-posed, are two contributing factors that lead to blurred object boundaries in ECT images. The ECT technique is based on the Lorentz reciprocity theorem, which detects scalar data. To improve the ability to recognize the object boundaries, we propose a permittivity imaging method based on the sensitivity matrix gradient. We use the sensitivity matrix gradient and the capacitance gradient to reconstruct the permittivity. The proposed method is a representation of ECT based on electromagnetic momentum (ECT-EMM). The ECT-EMM method is based on the electromagnetic momentum reciprocity theorem, which detects vector data. In this article, the principles of ECT-EMM under the electrodes-moving scheme and the object-moving scheme are derived. The object-moving scheme is employed for numerical simulation and experimental validation using the Tikhonov regularization algorithm. The reconstruction results show that compared with the ECT technique, the proposed method clearly distinguishes the object boundaries and has strong noise immunity.