International Society for Industrial Process Tomography

A Fast Iterative Adaptive Thresholding Algorithm for Electrical Resistance Tomography

Shengnan Zhang, Yanbin Xu^*, Feng Dong

Tianjin Key Laboratory of Process Measurement and Control

School of Electrical and Information Engineering, Tianjin University, Tianjin, P.R. China

^*Email: xuyanbin@tju.edu.cn

ABSTRACT

Regularization method is investigated extensively to solve the ill-posed inverse problem of electrical resistance tomography (ERT). Due to the sparsity property and the discrete characteristic of the electrical field, the sparse regularization algorithms with sparsity constrain are studied to improve the quality and efficiency of ERT problem. The iterative shrinkage thresholding algorithms (ISTA) have been applied to deal with the sparse regularization. However, the quality of the reconstructed images varies with the adopted regularization parameter and regularization form, and that the selection of thresholding parameter is difficult. Therefore, a fast iterative adaptive thresholding algorithm (FIATA), which can update the thresholding function adaptively according to the sparsity of the solution during the iteration process is proposed for ERT. This proposed method is demonstrated with several conductivity distributions both in simulation and experiment, and the reconstructed images are compared with that of FISTA algorithm. The images reconstructed by FIATA algorithm have shown a good performance whether in size or in location of the object. It is found that more penalty is implemented with a larger thresholding when the sparsity of the solution is large and less penalty with a smaller thresholding is implemented when the sparsity of the solution is small, which provides a more accurate result. Furthermore, the proposed FIATA method is expected to be applied to image reconstruction in other modalities.

Keywords Electrical resistance tomography, Inverse problem, Sparsity constrains, Adaptive thresholding algorithm

Industrial Application: Image Reconstruction