A Primal Dual Interior Point Framework for EIT Reconstruction with Automatic Regularization
The spatial resolution of the reconstructed images in Electrical impedance tomography (EIT) is low and a priori information regarding smooth conductivity changes limits reconstruction of sharp images while it is preferred in order to differentiate tissue boundaries in medical imaging. Measurement errors are another barrier that hinder a good image reconstruction. Generally l2 norms have been used due to computational convenience both for data and regularization terms which result in smooth solutions. However, the recent developments in optimization problem the Primal Dual-Interior Point Method (PDIPM) showed its effectiveness in dealing with the minimization problem. l1 norms on data and regularization terms in EIT image reconstruction address both problems of reconstruction with sharp edges and dealing with the electrode errors.
We demonstrated general formulation of the Primal-Dual Interior Point framework for EIT image reconstruction. We systematically evaluated the PDIPM algorithms with l1 and l2 norm based minimization in EIT inverse problems with automatic regularization based on a balancing principle. The performance of algorithms was evaluated in 4 scenarios in simulation. Finally we demonstrated its applicability for medical EIT through results from dog breathing experiments. The results show that the l1 minimization for EIT image reconstruction produced sharp edge and proved to be robust against measurement errors.