### Advancements in 3D Electromagnetic Tomography  
Traditional 2D EMT systems non-destructively capture two-dimensional gray-scale images of the measured cross-section. Generally, EMT coils are designed to be installed around the cross-section being measured, which is convenient for generating an excitation field and measuring the shape and size of the target from the tomographic image. Nonetheless, traditional 2D systems face two primary challenges:  
* It is impossible to obtain a complete 3D description of the whole object. The present technology is limited to integrating a series of two-dimensional images within the human mind to approximate a three-dimensional structure. Therefore, there is a desire to obtain intuitive and accurate three-dimensional images that display the spatial structure of the object under inspection, providing richer information than two-dimensional images. * Although the 2D system can reconstruct two-dimensional gray-scale images, the detection targets are definitively distributed in three dimensions. Unlike CT, EMT is a soft field, which means that the image reconstruction process is ill posed. In other words, the reconstructed two-dimensional sectional distribution is influenced not only by the object's actual distribution on that section but also by the coupling effect of the three-dimensional distribution surrounding the section. In light of this consideration, studying the three-dimensional distribution of the target is a more straightforward process than reconstructing two-dimensional images. In the preliminary phase of research on 3D EMT, explorations were conducted through both 2.5-dimensional (2.5D) approaches and direct 3D reconstruction. The first approach is pseudo-three-dimensional, or 2.5D imaging, which involves obtaining a series of 2D tomographic images at different radial heights based on 2D image reconstruction methods. Subsequently, the 2D image sequence is processed using contour splicing and Marching Cubes algorithms for interpolation to reconstruct the 3D image. Direct 3D reconstruction can generate images during the reconstruction process by measuring the electrical signal within the same layer and different layers. In contrast to the former, it obviates the need for intermediary steps, such as two-dimensional tomographic imaging and interpolation, that introduce errors. Our previous work has elucidated the advantages of direct 3D image reconstruction over 2.5D image reconstruction [15]. The EMT sensor has 12 coils, and image reconstruction was performed using the Tikhonov regularization method, the Projected Landweber iterative algorithm, and the total variation regularization method. Wei H.Y. proposed a matrix-free reconstruction method that addresses the problems of large-scale inversion in magnetic induction tomography [13]. Soleimani introduced a numerical solution for solving three-dimensional magnetostatic permeability tomography [16]. In light of the characteristics of metal defects, which are sparse, delicate, and concentrated on the surface, Wang Qi designed a \(3\times 3\) matrix-distributed sensor array and proposed a sparse regularization method, and they discussed the relationship between the excitation frequency and the detection depth. Simulation and experimental results demonstrate that the total variation regularization algorithm can accurately reconstruct the distribution of sample defects [17]. To improve the central area sensitivity (CAS), Martin Klein designed an excitation coil with spatial undulations, significantly enhancing the CAS by more than 20 dB compared to a traditional circular coil setup [18]. This enhancement allows the central region of a voluminous object with low conductivity to be clearly discernible above the noise floor, a fact that is confirmed by practical measurements. In biomedicine, particularly in the study of cerebral hemorrhage, three-dimensional imaging has been thoroughly investigated.