A New Truncation Strategy for Regularized D-Bar Method Used for ERT Image Reconstruction

Abstract

As a direct reconstruction method, D-bar method can reconstruct the conductivity distribution for electrical resistance tomography (ERT) without using sensitivity matrix. However, due to the ill-conditioned property of ERT inverse problem, the image reconstruction quality of D-bar algorithm is not high when the measured data contain noise. Meanwhile, the selection of truncation in the calculation of scattering transform by D-bar method in existing researches is based on experience. Focusing on the problems, a new truncation strategy for regularized D-bar method for ERT image reconstruction is proposed in this paper. On the basis of applying the Tikhonov regularization theory to solve the scattering transform of D-bar algorithm, a new relation between the noise level related to Dirichlet-to-Neumann (DN) map and the truncation is established. By comparing the imaging results of Tikhonov regularized D-bar method with the original D-bar method, it can be shown that the new approach has better performance in the direct reconstruction of conductivity distribution for ERT. The simulation and experimental results also show that the truncation selected according to the new relation in this paper can achieve high image quality for both two methods, which confirms the effectiveness of the proposed truncation strategy.