# Multi-Objective Robust Optimization Reconstruction Algorithm for Electrical Capacitance Tomography
## 7 Validation and Discussion
### Results and Discussion
#### 7.5.4 Reconstruction Time  
In the research and application of iterative algorithms, imaging time is one of the core metrics for evaluating algorithm performance. This is especially true in dynamic, rapidly changing scenarios where the importance of imaging speed is more pronounced. For these scenarios, measurement technologies need to have high-speed and real-time data processing capabilities to meet the stringent response speed requirements of practical applications.  
In the reconstruction tasks shown in Figure 3a-e, the MOROR algorithm's reconstruction times are approximately 0.0472 s, 0.0414 s, 0.0442 s, 0.0449 s, and 0.0433 s, respectively, showing fairly consistent and fast reconstruction capability. While certain algorithms may achieve shorter reconstruction times compared to the MOOR algorithm, their reconstruction quality is notably inferior. A meaningful comparison of reconstruction times can only be made when the quality of the reconstructions is on par.  
The reconstruction time of the MOROR algorithm is mainly spent on solving the LLOP. This is because the algorithm is designed to offload other computational tasks such as model  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Noise Levels** & **Object 1** & **Object 2** & **Object 3** & **Object 4** & **Object 5** \\ \hline
5\% & 0 & 0 & 0.28 & 0.46 & 0.27 \\
10\% & 0 & 0 & 0.39 & 0.99 & 0.63 \\
15\% & 0 & 0 & 0.91 & 1.21 & 1.14 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Image errors of the MOROR algorithm at different capacitance noise levels (%).  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Noise Levels** & **Object 1** & **Object 2** & **Object 3** & **Object 4** & **Object 5** \\ \hline
5\% & 1 & 1 & 1 & 0.9999 & 1 \\
10\% & 1 & 1 & 1 & 0.9998 & 0.9999 \\
15\% & 1 & 1 & 0.9998 & 0.9996 & 0.9996 \\ \hline \hline \end{tabular}
\end{table}
Table 8: Correlation coefficients of the MOROR algorithm at different capacitance noise levels.  
training and model parameter learning as much as possible, concentrating more computing resources on the online reconstruction process. However, despite the MOROR's simplified iterative structure, its iterative nature still poses challenges to real-time imaging. These challenges arise from the inherent conflict between two competing objectives: increasing the reconstruction speed and reducing the reconstruction error. Effectively balancing these two objectives remains an unresolved challenge in the field of iterative algorithms, and this limitation also hinders the broader adoption of electrical capacitance tomography technology in real-world industrial and scientific applications. The real-time imaging demands of rapidly changing scenes intensify this contradiction, making it difficult for traditional methods to maintain both accuracy and efficient computational performance.  
Enhancing the reconstruction speed typically involves simplifying models or decreasing the number of iterations, which can compromise accuracy. On the other hand, striving for high accuracy often results in greater computational complexity and longer processing times. This inherent conflict is one of common obstacles faced by iterative algorithms and is a core challenge that the MOROR algorithm needs to address in further optimization. There is still room for optimization in the MOROR algorithm. Future research will focus on developing more efficient solving strategies to shorten the reconstruction time.