Fast Electrical Impedance Tomography With Hybrid Priors

Electrical impedance tomography (EIT) is a non-ionizing and non-invasive imaging technique that reconstructs the electrical conductivity patterns within an object. Due to its low cost, real-time nature and portability, it is popular in a variety of applications ranging from medical imaging to industrial monitoring and geoscience. When electrical currents are injected, EIT reveals the internal conductivity distribution through boundary voltage measurements. However, EIT image reconstruction is an ill-posed problem due to the significant disparity between sparse boundary voltage measurements and the desired high-resolution conductivity images. Both conventional and deep learning approaches have been developed to address this challenge, primarily through spatial regularization and image regression techniques. While conventional methods employing regularizers can generate physically plausible conductivity distributions, their linear nature often limits reconstruction accuracy. Deep learning models achieve superior results but require substantial training datasets. In this work, we propose a novel iterative conductivity image reconstruction method for EIT, termed PnPEIT, which integrates both handcrafted and plug-and-play (PnP) priors within the alternating direction method of multipliers (ADMM) framework. Specifically, the objective function of PnPEIT contains the voltage reconstruction error and a sparse constraint, a graph regularization, and a PnP prior to the conductivity images. Next, the PnP prior term is optimized by a denoising operator and implemented by block-matching and 3D filtering (BM3D) or pre-trained denoising networks. Through alternating iterations, the algorithm converges rapidly and the desired conductivity image is obtained. Moreover, we provide a simple proof that the graph Laplacian regularization is not only equivalent to the non-local means denoising algorithm, but also accelerates convergence. Experiments on both synthetic and real-world datasets emphasize the advantage of the proposed method over traditional and cutting-edge EIT image reconstruction approaches.