A fast Tikhonov regularization method based on homotopic mapping for electrical resistance tomography

Electrical resistance tomography (ERT) is considered a novel sensing technique for monitoring conductivity distribution. Image reconstruction of ERT is an ill-posed inverse problem. In this paper, an improved regularization reconstruction method is presented to solve this issue. We adopted homotopic mapping to choose the regularization parameter of the iterative Tikhonov algorithm. The standard normal distribution function was used to continuously adjust the regularization parameter. Subsequently, the resultant image vector was deployed as the initial value of the iterative Tikhonov algorithm to improve the image quality. Finally, the improved method was combined with a projection algorithm based on the Krylov subspace, which was also effective in reducing the computational time. Both simulation and experimental results indicated that the new algorithm could improve the real-time performance and imaging quality.