# Multi-Objective Robust Optimization Reconstruction Algorithm for Electrical Capacitance Tomography
## 2 Related Work
Biased or unbalanced data can affect performance, and the results may be unpredictable, increasing usage risks. Surrogate optimization uses surrogate models to approximate the objective function, reducing computational loads [33; 34]. It excels with non-convex or non-smooth functions and allows the integration of various models and techniques. However, constructing high-quality surrogate models requires significant prior knowledge and training data, adding computational burdens. The performance depends on the distribution and quantity of initial samples, and poor sampling can bias the model. As dimensionality increases, the training difficulty and costs rise, and potential inaccuracies may lead to local optima. Despite these challenges, surrogate optimization shows great potential in image reconstruction. Deep learning, a powerful data-driven approach, excels in learning the complex nonlinear relationship between the capacitance and dielectric constant, offering efficient solutions for image reconstruction and inverse problems [35; 36; 37; 38]. Unlike traditional methods, it enables automated feature extraction and representation learning, significantly advancing electrical capacitance tomography [35; 36; 37; 38] and other fields [39; 40; 41; 42; 43; 44; 45; 46]. Deep learning models optimize parameter selection and address high real-time requirements by training on large datasets. However, challenges remain, including difficulty in capturing causal relationships, the risk of over-fitting with insufficient or low-quality data, and weak adaptability to changing environments [47]. Changes in measurement scenarios may require retraining, increasing costs and limiting practical applications in dynamic conditions. Despite these challenges, deep learning holds promise for improving intelligent measurement and imaging technologies, though improvements are needed in causality capture, environmental adaptability, and generalization capability. Several advanced techniques integrate deep learning with iterative methods, such as plug-and-play prior [48], algorithm unrolling [49; 50], and regularization by denoising [51]. These approaches achieve performance improvements for complex tasks such as image reconstruction. The plug-and-play prior provides a versatile framework for various applications through the flexible integration of prior information. The algorithm unrolling method converts optimization algorithms into neural networks, allowing end-to-end training and improved efficiency. Regularization by denoising uses denoisers to design the regularization term in order to bolster model robustness in noisy environments. Despite their success, these methods face challenges like high computational complexity and immature theoretical foundations, necessitating further exploration to improve effectiveness in practical applications [52]. The algorithms discussed have distinct advantages, limitations, and applicable conditions, showing performance variability across real-world scenarios. However, they fall short of achieving fully automated and precise image reconstruction. Currently, such processes depend on simplified analysis and empirical adjustments, limiting algorithm adaptability and performance under complex conditions. To improve image reconstruction quality, innovation in imaging strategies is crucial, rather than refining existing methods. This research aims to achieve this by introducing multidisciplinary approaches combining advanced optimization, multimodal learning, and measurement physics to enhance image reconstruction accuracy. Further technical details will be explored in subsequent sections.