Image Reconstruction of Conductivity Distribution With Combined L1-Norm Fidelity and Hybrid Total Variation Penalty

Image reconstruction of conductivity distribution is a highly nonlinear ill-posed inverse problem in electrical impedance tomography (EIT). To solve the problem, Tikhonov regularization and total variation (TV) regularization methods have been generally adopted. However, reconstructed images suffer from excessive smoothness or staircase effect. In this article, a novel approach is proposed for imaging conductivity distribution. Unlike traditional regularization methods, fidelity term based on $L_{1}$ -norm is introduced to stabilize the ill-posed problem and enforce sparsity in the solution. Moreover, a first-order and high-order TV combined hybrid penalty term is introduced to keep the sharp profile and restrain the staircase effect. During image reconstruction, regularization parameter and weighting factor are determined by the adaptive method. In addition, a soft-thresholding operator is introduced to remove artifact and enhance robustness to noise. Numerical simulations have been performed to validate the performance of the proposed approach against Landweber, Tikhonov, TV, high-order TV, and iterated soft-thresholding methods. The impacts of conductivity distribution, conductivity contrast, contact impedance, and boundary shape on reconstruction are studied. Besides, robustness to noise and computation time are evaluated. The performance of the proposed approach is also verified by phantom experiments. Simulation and experimental results demonstrate that the proposed approach performs well in image reconstruction of conductivity distribution. Clearer background is observed and inclusions with sharp or smooth edges can be better reconstructed.