# Electromagnetic Imaging of Uniaxial Objects by Two-Step Neural Network
## 1 Introduction  
Electromagnetic imaging is an advanced technique that entails evenly distributing transmitter and receiver antennas around a scatterer widely employed in biomedical imaging [1], remote sensing [2], non-destructive testing [3], etc. By illuminating an unknown scatterer with electromagnetic waves and capturing the reflected scattered field, valuable information regarding its size, shape, and material composition can be reconstructed. Due to the highly nonlinear nature of inverse scattering problems (ISPs), iterative algorithms with regularization are frequently utilized to address them. Electromagnetic imaging algorithms generally fall into two categories: (1) Approximation methods [4, 5]: Traditional techniques demonstrate significant inversion capabilities, particularly with small scatterers or low-contrast objects. Accuracy will diminish significantly when the size or contrast becomes larger due to the multiple scattering effect. (2) Iterative methods [6, 7, 8, 9]: These methods can achieve higher accuracy by minimizing the mismatch error between inversion and measurement results. Considering the inherent ill-posedness of the ISPs, incorporating a regularization term into the cost function is crucial to stabilize the optimization process. However, challenges such as high computational costs and low iterative convergence will hinder instant inversion tasks. Convolutional neural networks (CNNs) have been widely utilized in image and speech recognition recently, yielding promising results. There are three main categoriesof learning methods: (1) Direct learning methods [10; 11; 12; 13; 14; 15; 16]: These methods employ neural networks directly to learn wave equations and solve them. (2) Learning-assisted objective function methods [17; 18; 19; 20; 21]: Neural networks are used iteratively in the training process for image reconstruction. (3) Physics-assisted learning methods [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32]: This method applies [PERSON]'s equations to pre-calculate certain physical quantities. Neural networks are subsequently employed to compute more precise physical quantities to achieve better reconstruction of objects. In 2020, [PERSON] introduced a two-stage model to solve ISPs. His approach involved developing an autoencoder to convert high-resolution vectors in the first stage, followed by creating a second neural network to correlate microwave signals with the compressed features. The numerical results indicated that the deep learning network developed by [PERSON] could accurately identify objects of similar complexity levels across the entire domain of interest [14]. In 2021, [PERSON] proposed a modified contrast scheme utilizing convolutional neural networks to handle the high nonlinearity present in electromagnetic imaging. The numerical findings suggested that this modified contrast scheme, when combined with convolutional neural networks, could get rid of nonlinearity effectively [28]. In 2022, [PERSON] combined the visual geometric group and the total variation loss function to reconstruct biaxial objects with a generative adversarial network (GAN). The experimental results show that this method requires a long training time, but it has good image reconstruction capabilities [29]. In 2023, [PERSON] combined a weighted loss function composed of adversarial loss, mean absolute percentage error (MAPE), and structural similarity (SSIM) into a generative adversarial network with a self-attention mechanism. The numerical results show that the proposed architecture exhibits good generalization ability and stability [31]. Recently, the convergence of electromagnetic imaging (EMI) technology with the Internet of Things (IoT) has sparked a wave of innovation across multiple sectors. This amalgamation offers unprecedented opportunities for real-time monitoring, predictive maintenance, and enhanced decision-making processes. As the world becomes increasingly interconnected, the integration of EMI with the IoT presents a transformative paradigm that transcends traditional boundaries.