Electrical impedance tomography with multiplicative regularization

In this work, a multiplicative regularization scheme is applied to EIT data inversion. A weighted L2-norm-based regularization with edge-preserving characteristics is used as a multiplicative constraint. In this scheme, the setting of regularization parameter in the cost functional is avoided, and the relative weights between the data misfit and the regularization can be adjusted adaptively during the inversion. In this work, Gauss-Newton method is used to minimize the cost functional iteratively. In the minimization process, the gradient of the regularization factor needs to be computed. This requires discrete representation of gradient and divergence operators on triangular or tetrahedral meshes. To this end, a method based on the theory of discrete exterior calculus (DEC) is introduced to rigorously describe these operators on meshes. The inversion algorithm is tested using both synthetic and experimental data. The results show good edge-preserving and anti-noise performance of the multiplicative regularization in the EIT inverse problem.