# Complex-Valued CNN-Based Defect Reconstruction of Carbon Steel from Eddy Current Signals
## 4 Results
### Defect Reconstruction Results  
For defect diameters of 10 mm in length, both in the inductive and resistive components, the results are shown in Figures 7 and 8.  
In the inductive component, as shown in Figure 7, the defect signals became clearer as the excitation frequency gradually increased; especially at the low frequency of 5 kHz,  
Figure 8: Two-dimensional contour plots of pancake coil resistance at different excitation frequencies for EDM recesses with depths from 0.5 mm to 3.0 mm and lengths of 10 mm: (**a**): 5 kHz; (**b**): 20 kHz; (**c**): 80 kHz; (**d**): 320 kHz.  
Figure 7: Two-dimensional contour plots of pancake coil inductance at different excitation frequencies for EDM recesses with depths from 0.5 mm to 3.0 mm and lengths of 10 mm: (**a**): 5 kHz; (**b**): 20 kHz; (**c**): 80 kHz; (**d**): 320 kHz.  
the defects with a depth of 0.5 mm were not detected effectively, which indicates that the sensitivity of the low frequency to such defects is poor. As the frequency increased, especially at 80 kHz and 320 kHz, the defect signals were significantly enhanced to detect defects of all depths, and the clarity of the defect signals gradually improved as the excitation frequency increased. This indicates that the high-frequency eddy currents are more sensitive to small defects and are able to more accurately detect tiny defects on the surface and in shallow superficial layers.  
In the resistive component, as shown in Figure 8, at an excitation frequency of 5 kHz, the signals of the smallest defects were relatively weak and almost undetectable. However, as the excitation frequency increased, the detection of defect signals improved significantly, especially at 80 kHz and 320 kHz, where all defects could be detected and the signals showed clearer fluctuations, suggesting that these frequencies were more suitable for detecting defects in the middle to shallow layers.  
Figure 9 presents the reconstructed defect images for a 10 mm flaw at 5 kHz. Compared with the original eddy current signal maps, the reconstructed results exhibit significantly enhanced defect features, indicating that the proposed method greatly improves defect visualization and recognition. The background noise is effectively suppressed, and the defect boundaries appear much sharper, resulting in clearer and more accurate shape contours. This improvement is particularly important for nondestructive evaluation applications, where the precise geometric characterization of defects is crucial for assessing structural integrity. Moreover, the reconstructed images reveal more defined internal defect structures, which are often obscured in raw impedance maps due to signal distortion or interference. This implies that the complex-valued convolutional operations successfully capture essential morphological details from both the amplitude and phase components. In addition, the inter-class differences among various types of flaws become more distinguishable in the reconstructed feature space. Subtle variations in size, orientation, and depth are more clearly represented, facilitating better separation and recognition by the downstream classification model. These enhancements not only benefit the visual interpretability of defect maps but also increase the model's discriminative ability across multiple defect types. Overall, the results demonstrate the effectiveness of the proposed CV-CNN-based reconstruction in generating high-fidelity and diagnostically meaningful representations of eddy current signals.  
Figure 9: Two-dimensional contour plots of pancake coil reconstructed defect image for EDM recesses with depths from 0.5 mm to 3.0 mm and lengths of 10 mm.