Fig. 3: Quantitative imaging of virtual gas-liquid flows by Deep Back Projection (DBP) with 50 dB Signal-Noise Ratio (SNR).

a Two representative sets of sequential gas-liquid flows generated by three-dimensional Fluid-Electrostatic field Coupling Model (3D-FECM) and corresponding image reconstruction results of DBP. For the sequential gas-liquid flows in (i), the pipe is initially filled with liquid. For the sequential gas-liquid flows in (ii), the pipe is initially filled with gas. 3D dynamic liquid phase distributions in the ECT sensing region can be converted to the 2D volume-averaged liquid phase distributions as the ground truth (see (iii)). The cross-section images reconstructed by DBP for the gas-liquid flows in (iii) are presented in (iv). b Quantitative imaging of virtual gas-liquid transient flow with high temporal resolution (200 frames per second). (v) The authentic liquid phase distributions for evaluating the performance of image reconstruction. (vi) The images reconstructed by DBP for the gas-liquid flows in (v). The cross-section images in (vi) are a set of representative images selected from the continuous reconstruction results. (vii) The Structural Similarity Index Measure (SSIM) and Root Mean Square Error (RMSE) of the DBP results in (vi).