An experimental clinical evaluation of EIT imaging with ℓ1 data and image norms

Electrical impedance tomography (EIT) produces an image of internal conductivity distributions in a body from current injection and electrical measurements at surface electrodes. Typically, image reconstruction is formulated using regularized schemes in which ℓ2-norms are used for both data misfit and image prior terms. Such a formulation is computationally convenient, but favours smooth conductivity solutions and is sensitive to outliers. Recent studies highlighted the potential of ℓ1-norm and provided the mathematical basis to improve image quality and robustness of the images to data outliers. In this paper, we (i) extended a primal-dual interior point method (PDIPM) algorithm to 2.5D EIT image reconstruction to solve ℓ1 and mixed ℓ1/ℓ2 formulations efficiently, (ii) evaluated the formulation on clinical and experimental data, and (iii) developed a practical strategy to select hyperparameters using the L-curve which requires minimum user-dependence. The PDIPM algorithm was evaluated using clinical and experimental scenarios on human lung and dog breathing with known electrode errors, which requires a rigorous regularization and causes the failure of reconstruction with an ℓ2-norm solution. The results showed that an ℓ1 solution is not only more robust to unavoidable measurement errors in a clinical setting, but it also provides high contrast resolution on organ boundaries.