Sensitivity matrix construction for electrical capacitance tomography based on the difference model

Image reconstruction for electrical capacitance tomography (ECT) is an inherently nonlinear and ill-posed inverse problem. Reconstruction methods based on a linear approximation widely are adopted. In this paper, that the gradient of the sensitivity function is related to the severity of nonlinearity between measured capacitances and permittivity distribution is explored, and the gradient magnitude of the sensitivity is used for the sensitivity normalization process to improve the fidelity of the linear approximation. Then, a new sensitivity normalization model — the difference normalization model is proposed, which combines both parallel and series normalization models with the central difference of the sensitivity to achieve better approximation. Given a comparison of sensitivities based on three normalization models, the features of sensitivity associated with the difference models are discussed. With the new method, the reconstruction performance of those conventional iterative algorithms using sensitivity maps, such as Landweber iteration method and iterative Tikhonov regularization (ITR), is improved significantly without increasing computational burden.