A new regularization algorithm based on the neighborhood method for electrical impedance tomography

Abstract

Regularization can be used to address the ill-posed inverse problem of electrical impedance tomography (EIT). However, the most commonly used regularization methods have their own inherent issues, such as the over-smoothness of reconstructed edges and unstable solution due to measurement noise. In this paper, a new regularization method is proposed, which utilizes the total differences of neighboring pixels (TDN) as the penalty term by utilizing spatial constraints from four or even more directions. With the use of more effective spatial constraints, the solution can be kept more stable. To obtain the sharp edges between different materials in the reconstructed image, the L1 norm was utilized as the form of the penalty term. Moreover, targeting the reconstruction of square objects, an improved image reconstruction approach based on this method was investigated. Two new criteria for the evaluation of reconstruction quality were proposed accordingly. The simulation and experimental results demonstrated that the TDN regularization performed robustly against the boundary measurement noise as well as possessing the ability to preserve the relatively sharp edges of interesting objects.