# Algorithms in Tomography and Related Inverse Problems--A Review
## 5 A Deep Learning-Based 3D Ground-Penetrating Radar Data Inversion  
Ground-penetrating radar (GPR) has found extensive use in geophysical exploration and civil engineering applications owing to its cost-effectiveness and non-destructive properties. The reconstruction of 3D permittivity maps from GPR data is invaluable for extracting crucial information about subsurface objects. These maps offer insights into various aspects, including the shapes, sizes, positions, orientations, and permittivity properties of these subsurface entities. Numerous conventional algorithms have been developed for reconstructing 3D subsurface images from GPR C-scans. These migration algorithms offer approximations of object positions and shapes but do not provide detailed permittivity maps. The permittivity data are vital for tasks such as object identification and health assessments. To address the challenge of reconstructing subsurface permittivity maps, a full-wave inversion (FWI) algorithm was introduced in [119; 120; 121; 122]. This algorithm enables the reconstruction of subsurface structure permittivity maps from GPR data through a nonlinear least-squared optimization process. However, processing 3D GPR data with the 3D FWI method can be computationally intensive. To enhance efficiency, a modified total variation (MTV) regularization scheme was introduced [123]. It is noteworthy that only two studies have applied 3D FWI to reconstruct subsurface permittivity or conductivity distributions from GPR data. The high computational complexity and limited applicability of FWI algorithms have posed challenges in their use for reconstructing intricate 3D subsurface scenarios. In recent times, the integration of deep learning methodologies has emerged as a viable solution to tackle challenges in inverse scattering and electromagnetic (EM) imaging domains [124; 125; 126]. These investigations encompass a spectrum of approaches, ranging from entirely data-driven techniques to those that blend physics-based insights. They have exemplified the remarkable effectiveness of deep learning in addressing a wide array of EM inverse problems. The utility of deep learning-based methods has also extended to GPR applications [127; 128], with a particular emphasis on resolving GPR inverse problems, including image classification, signature recognition, subsurface object detection, and the restoration of object properties [129; 130; 131; 132; 133]. Within this context, Deep Neural Networks (DNNs) have been harnessed to reconstruct 2D subsurface permittivity maps based on GPR B-scans [134; 135; 136; 137]. However, it is worth noting that the scope of these endeavors has been confined to the restoration of 2D domain permittivity maps. Consequently, they offer insights primarily at the sectional level of subsurface scenarios, leaving room for improvement in capturing critical details such as object orientation and shape, especially when dealing with intricate subsurface structures. Furthermore, it is crucial to recognize that the use of full-wave simulations for 2D inversion may not faithfully replicate the intricacies of EM phenomena in the actual 3D world. In the 2D modeling paradigm, assumptions are made, including the invariance of scattering in one coordinate direction, the treatment of line sources as infinitely long, and the limitation to linear polarization. These assumptions deviate from the reality of complex 3D modeling scenarios, potentially yielding results that diverge significantly from actual 3D modeling outcomes [122]. Therefore, it becomes imperative to explore the potential of deep learning techniques in the reconstruction of 3D subsurface permittivity maps, transcending the limitations of 2D reconstruction and offering a more accurate representation of real-world EM phenomena. A significant obstacle in the reconstruction of subsurface permittivity maps is the interference posed by various noise patterns. These include direct coupling, reflections from the ground, and environmental noise, which can obscure object reflections in GPR data.