An Inverse Solution for 2D Electrical Impedance Tomography Based on Electrical Properties of Material Blocks

A non-iterative linear inverse solution for the block approach in EIT

“…In the first part, using the EIT forward solution, a phantom model has been constructed with known boundary values. In the second part, using the data in the first part, inverse problem is solved by non-linear solution method [19]. In the third part using the data in the first part inverse problem is solved by proposed method on this article (linear method).…”

“…Similarly, e x (i,j) and e y (i,j) are the voltages of the edge-centres for the B(i,j) block. For B(i,j) block following equations are true [19]:…”

“…However in some papers RMSE has been adopted as a comparison factor [19,[22][23][24][25][26]. For example 10 −1 to 10 Shape estimation by EKF for dynamic EIT [24] 10 −2 to 10 −1 Employing IMM, EKF and CCEKF for dynamic EIT [23] 10 −2 to 10 −1 Neural networks and front point approach [25] 10 −2 to 10 −1 Interpolation of front points method [22] 10 −5 to 10 −3 Non-linear block method [19] 10 −5 to 10 −4 Proposed linear block method (this paper) 10 −8 to 10 −7 in a work conducted by Kim for 2D EIT inverse problem, applying interpolation of front points method for approximation of regions of inner object results in RMS on order of 10 −5 to 10 −3 for reconstructed image [22]. Also, using neural networks and front point approach for estimation of 2D EIT image results 10 −2 to 10 −1 in RMSE [25].…”

“…In block method, a rectangular shape subject is divided into m × n similar size blocks with same electrical impedances in each block [19] as shown in Fig. 1A.…”

“…They solve the nonlinear problem, so they have the potential of finding the conductivity values with high accuracy. Examples of direct algorithms based on numerical techniques may be found at Mueller's work [18] or in block method for a rectangular shape subject [19].…”