Total Variation Regularization Based on Iteratively Reweighted Least-Squares Method for Electrical Resistance Tomography

Abstract

The regularization method has been utilized to address the ill-posed inverse problem of electrical resistance tomography (ERT). As one of the regularization methods, the total variation (TV) regularization method has the advantage of edge-preserving. A majority of research has been focused on the study of the penalty term in the TV method. In this article, a novel TV regularization based on iteratively reweighted least squares (TV-IRLS) method is proposed, in which, $L_{1}$ -norm is applied to the fidelity term, and a weighting matrix is applied to convert the $L_{1}$ -norm to $L_{2}$ -norm when calculating the objective function, which reduces the difficulty of solving the $L_{1}$ -norm. An improved generalized cross-validation method is adopted to determine the optimal regularization parameter (RP) automatically, and an automatic method is presented for the selection of the threshold value in the weighting matrix to guarantee the accuracy and speed of the solution. Meanwhile, a scaling factor is introduced to constrain the solution and ensure the stability of the solution. For verifying the performance of the proposed TV-IRLS regularization method, both numerical simulation and static experiments are carried out in the image reconstruction of ERT through qualitative and quantitative analysis. The results demonstrate that the proposed TV-IRLS regularization method performs well in improving the quality and resolution of the reconstructed images in ERT. Besides, it is more robust to data noises compared with the Tikhonov regularization method and TV regularization method.