# Multi-Objective Robust Optimization Reconstruction Algorithm for Electrical Capacitance Tomography
## 7 Validation and Discussion
### Results and Discussion
#### 7.5.1 The Results of the Iterative Reconstruction Algorithms  
The primary objective of this section is to conduct a comparison between the MOROR algorithm and iterative algorithms. We conduct an in-depth analysis of their performance across different reconstruction scenarios while systematically examining their respective strengths and limitations. The critical parameters used throughout the reconstruction procedure are delineated in Table 2. The selection of these parameters not only affects the accuracy and efficiency of the algorithms but also plays a decisive role in determining the reconstruction quality. Through this comparative analysis, we gain enhanced insights into the applicability scope of each algorithm and identify potential optimization directions for future improvements. In the MOROR algorithm, the algorithm parameters are estimated by solving Equation (12) with \(\mathcal{W}_{i}^{k+1}=  
Figure 4: Images reconstructed by (**a**) L\({}_{1.2}\)R, (**b**) L1R, (**c**) FL1R, (**d**) LRR, (**e**) PRPCG, (**f**) L\({}_{1/2}\)R, (**g**) TL1R, and (**h**) MOROR. From the results shown in Figure 4 and Tables 3 and 4, it is evident that the algorithms being compared perform poorly in image reconstruction tasks and struggle to reconstruct high-quality images. In contrast, the MOROR algorithm performs excellently in image reconstruction tasks, achieving high-fidelity reconstruction. This conclusion is validated not only through subjective visual comparisons but also by the quantitative analysis results. The MOROR algorithm achieves a maximum image error as low as 0.39%, with a correlation coefficient peaking at 1. These numerical results clearly highlight the superior performance of the MOROR algorithm. Compared to existing reconstruction algorithms, the MOROR algorithm has made significant advancements in the design and solution of the reconstruction model and the exploration and integration of prior information, as well as the adaptive optimization of model parameters. The image reconstruction problem is modeled as a multi-objective robust optimization problem, which not only improves reconstruction accuracy and robustness but also provides a systematic reconstruction framework that facilitates parameter tuning and the optimization of reconstruction quality. In the MOROR algorithm, the LLOP integrates the MLPI, sparsity priors, and measurement principles, enhancing the diversity and complementarity of information in the reconstruction process, laying the foundation for reconstructing high-quality images. Specifically, the MLPI captures the statistical characteristics and patterns of the object to be reconstructed, not only integrating as a prior image into the reconstruction model, increasing the diversity and complementarity of prior information, but also serving as an ideal iterative initial value, improving the convergence of the algorithm. By integrating the MLPI, the fusion of measurement physics with multimodal learning is realized, contributing to a significant enhancement in reconstruction performance. The MOROR algorithm also realizes the adaptive selection of model parameters, facilitating the attainment of superior reconstruction results. Additionally, the adaptive learning of model parameters not only effectively eliminates the uncertainties caused by reliance on empirical selection methods, enhancing the model's level of automation, but also significantly boosts the model's ability to perform reconstruction tasks in complex environments. We propose a new MNN to infer the MLPI. This new MNN performs inference tasks by simultaneously utilizing image and capacitance data. It fully leverages information from different modalities, compensating for the shortcomings of single-modality information and reducing potential information loss that may occur when only using one type of modality data, thereby improving the overall performance of the model.