# Multi-Objective Robust Optimization Reconstruction Algorithm for Electrical Capacitance Tomography
## 2 Related Work  
Image reconstruction algorithms play a crucial role in determining the effectiveness of the measurement technology. In this section, we provide a comprehensive overview of the popular reconstruction algorithms, outlining their fundamental technical principles and discussing their advantages and limitations. We aim to summarize the key factors contributing to the success of these algorithms in specific applications, as well as the challenges they face in broader applications. Our discussion starts with a review of classical iterative approaches that exclude regularization terms, such as the Kaczmarz algorithm [1] and the Landweber algorithm [2]. These methods are widely recognized for their simple iterative structure, low memory consumption, and high computational efficiency. However, these two algorithms fail to incorporate prior information about reconstruction objects, which limits their ability to produce high-quality images. To address this limitation and enhance the stability of numerical solutions, iterative regularization methods have been developed. These methods employ either single [3; 4; 5; 6; 7] or multiple [8; 9; 10; 11; 12; 13; 14; 15; 16] regularization terms to better utilize prior information, narrow the solution space, ensure numerical stability, and enhance reconstruction quality and robustness. However, they rely on fixed model components and prior insights derived from theoretical analysis and empirical knowledge, which may not adequately capture the complexity of real-world reconstruction scenarios. The solution of non-convex or non-smooth regularization models complicates the development of numerical algorithms. In addition, choosing regularization parameters continues to be an unresolved problem. Recent advancements have witnessed the development of novel imaging algorithms [17; 18; 19] aimed at improving imaging quality. Non-iterative algorithms are a key category in image reconstruction methods, known for their lower computational complexity compared to iterative methods, making them advantageous for online reconstruction, particularly in real-time scenarios [20; 21]. These algorithms simplify physical or mathematical models to enhance computational efficiency but at the cost of precision, being more sensitive to noise and model errors. Despite these limitations, they are valuable in conditions requiring high real-time responsiveness but lower precision due to their efficiency and speed. Thus, it is important to balance the pros and cons of non-iterative algorithms based on specific measurement goals and conditions to choose the most suitable reconstruction method. Evolutionary algorithms, as population-based methods, have attracted increasing attention due to their independence from the differentiability of the objective function, allowing application across diverse scenarios [22; 23]. They excel in complex problems but face limitations such as slower convergence and reduced performance in high-dimensional tasks, like image reconstruction with many pixel variables. The effectiveness of evolutionary algorithms can also be hindered by challenging parameter settings. Despite these issues, improvement techniques are being developed to enhance their flexibility and adaptability in complex scenarios. Evolutionary multi-objective optimization algorithms are particularly effective for balancing multiple objectives in inverse problems but share limitations with single-objective approaches [24; 25]. New methods have been introduced to mitigate these issues [26; 27], offering new insights for advancing image reconstruction algorithm design. Generative models have been used to solve inverse problems, with different variants developed for various tasks [28; 29; 30; 31; 32]. Their main advantage is the ability to learn complex probability distributions, capturing both global and local image details. They generalize well to diverse challenges but face limitations like high computational costs, training instability, and reliance on large and high-quality datasets.