# Complex-Valued CNN-Based Defect Reconstruction of Carbon Steel from Eddy Current Signals
## 1 Introduction  
Non-destructive testing (NDT) is a class of techniques that is used to find internal or surface defects without destroying the integrity of the material or structure. Among the many NDT methods, eddy current testing (ECT) is widely used in aerospace, petrochemical, and other fields for component and pipe inspection due to its sensitivity to surface and near-surface defects in conductive materials [1]. Although traditional ECT techniques can effectively identify the presence of defects, there are obvious deficiencies in the extraction of defect geometrical information (e.g., size and shape), which is crucial for structural health monitoring (SHM) and remaining useful life (RUL) assessment. To overcome these limitations, researchers have gradually introduced deep learning methods, especially neural networks, to model and resolve the deep features in eddy current signals. In earlier studies, [PERSON] et al. [2] used neural networks to achievethe feature classification of multi-frequency eddy current signals, while [PERSON] et al. [3] accurately predicted the length and depth of cracks by back-propagation neural networks. To address the problem of blurred ECT images, [PERSON] et al. [4] combined image processing and neural network methods to achieve the high-fidelity recovery of the defect geometry. In addition, multi-task learning combined with deep neural networks has also been used to enhance detection robustness and classification efficiency [5] and the Lissajous graphical classification method proposed by [PERSON] et al. [6], and it significantly improves the efficiency of fast defect classification in ECT. The detection capability of ECT in various fields such as aerospace, pipelines, and thin film materials has also been significantly enhanced by the application of deep learning [7; 8; 9]. In recent years, there has been a rise in pictorial eddy current signal analysis methods, such as eddy current thermography and C-scanning, which help to visualize defect morphology more intuitively, and this type of representation in the form of images facilitates the application of deep learning methods in defect recognition [10]. Based on this, deep learning methods, especially convolutional neural networks (CNNs), have demonstrated strong capabilities in defect detection, classification and reconstruction. CNNs can automatically extract multi-scale spatial and temporal features implicit in ECT signals, breaking through the limitations of traditional signal processing methods in feature design and non-linear modeling. For example, the multi-scale spatio-temporal self-attention (MSTSA) network introduces spatial and temporal attention mechanisms into ECT signal processing, which significantly improves the accuracy and efficiency of defect recognition [11]. In addition, several studies have used neural networks for effective reconstruction and regression prediction of defect morphology, including inverse methods and finite element simulations to extract defect geometric features [12; 13; 14]. Multi-channel data fusion, image processing and feature learning have also been used for three-dimensional (3D) defect reconstruction and multi-scale defect recognition [15; 16; 17]. Meanwhile, neural networks have also been used in defect classification and multiparameter estimation tasks [18; 19; 20; 21; 22]. However, traditional CNNs mainly deal with real-domain signals and cannot fully utilize the magnitude and phase information in ECT signals, thus limiting their capability in high-resolution defect reconstruction. Some studies have begun to try to improve the reconstruction performance by using complex-valued modeling, such as mapping ECT signals into images and then performing convolutional processing, but still do not fully utilize the structural information in the complex-valued signals themselves [20; 22].