Three-Dimensional Electrical Impedance Tomography With Multiplicative Regularization

Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, Aria Abubakar

Abstract: Objective: The multiplicative regularization scheme is applied to three-dimensional electrical impedance tomography (EIT) image reconstruction problem to alleviate its ill-posedness. Methods: A cost functional is constructed by multiplying the data misfit functional with the regularization functional. The regularization functional is based on a weighted L2-norm with the edge-preserving characteristic. Gauss-Newton method is used to minimize the cost functional. A method based on the discrete exterior calculus (DEC) theory is introduced to formulate the discrete gradient and divergence operators related to the regularization on unstructured meshes. Results: Both numerical and experimental results show good reconstruction accuracy and anti-noise performance of the algorithm. The reconstruction results using human thoracic data show promising applications in thorax imaging. Conclusion: The multiplicative regularization can be applied to EIT image reconstruction with promising applications in thorax imaging. Significance: In the multiplicative regularization scheme, there is no need to set an artificial regularization parameter in the cost functional. This helps to reduce the workload related to choosing a regularization parameter which may require expertise and many numerical experiments. The DEC-based method provides a systematic and rigorous way to formulate operators on unstructured meshes. This may help EIT image reconstructions using regularizations imposing structural or spatial constraints.