Low-rank plus sparse matrix decomposition for 3D dynamic electrical impedance tomography

Abstract Motion tracking presents a significant challenge in particularly for three-dimensional monitoring of moving targets. Traditional imaging techniques lack sufficient speed for real-time applications, whereas electrical impedance tomography (EIT) offers radiation-free and rapid imaging capabilities ideal for dynamic monitoring. This paper introduces a three-dimensional low-rank plus sparse (3D-L+S) matrix decomposition algorithm for EIT, which effectively separates dynamic and background components in 3D impedance data collected through multi-wire electrodes. Unlike traditional methods, this approach simultaneously integrates spatial and temporal structural information. Our results demonstrate superior structural continuity and more coherent conductivity distribution in reconstructed 3D images compared to conventional algorithms, such as conjugate gradient and total variation regularization (TV) methods. Both simulation and experimental validations confirm the significant potential of the 3D-L+S approach for dynamic EIT reconstruction applications. The method shows particular promise for dynamic monitoring applications with relatively stable geometric configurations.