Total Variation Regularization Method with L1-Norm Fidelity Term for Electrical Tomography

Xizi Song, Yanbin Xu, ChaoTan and Feng Dong

Tianjin Key Laboratory of Process Measurement and Control

School of Electrical Engineering and Automation, Tianjin University, Tianjin, China xuyanbin@tju.edu.cn

ABSTRACT

Electrical tomography (ET) is a promising measurement technique, while its inverse problem is ill- posed. Total variation (TV) regularization method has been widely investigated to solve this ill-posed inverse problem, owing to its good ability of preserving edges. However, the conventional TV regularization method with L2-norm fidelity term (TV_L2) is of scale-dependent property, which means that the regularization intensity is inversely proportional to the scale of the inclusion and, compared with large-scale inclusion, small-scale inclusion is easier to lose for reconstructed image. To reduce its scale-dependent property, TV regularization method with L1-norm fidelity term (TV_L1) is investigated for ET. With weaker norm adopted as fidelity term, the fidelity and regularization terms scale with respect to each other is modified. As distinct from that with TV_L2, small-scale inclusion of reconstructed image with TV_L1 maintains contrast even with larger regularization factor. Therefore, the TV_L1 method is applicable for models with multi-scale inclusions. Simulation results of TV_L1 and TV_L2 methods demonstrate that this TV_L1 method can improve the resolution of reconstructed images.

Keywords Electrical tomography, Total variation regularization method, Image reconstruction, L1- norm