Analysis of Sensitivity Matrix for Electrical Resistance Tomography

Electrical Resistance Tomography (ERT) is a detection technique for reconstructing conductivity distribution from boundary measurements. However, the image reconstruction of ERT is an ill-posed and nonlinear inverse problem. There are many algorithms for solving inverse problems based on the sensitivity theory, the basic idea of which is to use the sensitivity matrix of reference field to represent the sensitivity matrix of the reconstruction process. However, this approximation of reconstruction process is based on the premise that the change of electrical conductivity distribution can be ignored and the distribution of sensitive field is approximately unchanged. The error introduced by using the sensitivity matrix of reference field for solving process cannot be ignored when the change of electrical conductivity cannot be ignored in the field. In order to optimize the solution process, this paper analyzes the factors that cause the solution error by the adopted sensitivity matrix and further explores the relationship between the sensitivity matrix and electrical conductivity distribution. The preliminary optimization direction of sensitivity matrix is also suggested.