2.1. The Structure of Sensors
The 16-electrode ERT and ECT sensors are depicted in Figures 1(a) and (b).
Figure 1. The structure of sensor: (a) ERT sensor and (b) ECT sensor
In ERT, the electrodes are mounted equally on the interior of pipe. The measured objects in pipe must be conductive and the electrodes must contact with them. While in ECT, the electrodes are mounted equally on the exterior of pipe. The measured objects in pipe must be nonconductive or most of the mixture of the multi-phase material is nonconductive.
2.2. Image Reconstruction Algorithms
There are many different image reconstruction methods for ERT and ECT, which can be mainly classified into two categories, direct methods (linear back projection, Tikhonov regularization and truncated singular value decomposition) and iterative methods (Conjugate Gradient and Landweber) (Yang & Peng, 2003; Marashdeh, Warsito, Fan, & Teixeira, 2006; Wang, Tang, & Cao, 2007). In our study, Landweber iterative algorithm with optimal step length was adopted which is defined as (Liu, Fu, & Yang, 1999):
(1) (2) (3) where
,
is the measurements,
is the step length and
is the normalized image grey in the
kth iteration, respectively.