Regularizing the Gauss­Newton Iterative Procedure for the Inverse Boundary Problem of ERT

Yaoyuan Xu, Feng Dong, Chao Tan

Tianjin Key Laboratory of Process Measurement and Control, School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Tel: 86­22­27890276, Fax: 86­22­27892055, Email: fdong@tju.edu.cn

ABSTRACT

Electrical resistance tomography (ERT) is a novel non­intrusive technique to image the electrical conductivity distribution. ERT image reconstruction is characterized as a severely nonlinear and ill­ posed inverse problem with many unknowns. In recent years, there are a growing number of papers published which aim to determine the locations and shapes of inclusions by assuming their conductivities are piece­wise constant and isotropic.

In this work, a Newton iterative algorithm is adopted to approximate the boundary of inclusions based on quadratic boundary element method. Two regularization methods are adopted, the first one is widely used Tikhonov regularization and the second one is based on Fourier decomposition in the polar coordinate. Although there are many criterions to determine the regularization parameter for the former, such as L­curve criterion, generalized cross validation (GCV) and so on, they are yet not always effective for regularizing this iterative procedure. A parameter selection is presented, which ensures the stability and also convergence performance. A skill for the selection of decomposition order for the latter method is given.

Keywords Electrical resistance tomography; Image reconstruction; Tikhonov regularization; Fourier decomposition