GPR 3D Image Reconstruction with Sparse Recovery for Random Spatial Sampling

Ground Penetrating Radar (GPR) is widely used for subsurface exploration in applications such as structural health monitoring, archaeological surveys, and the detection of buried objects. However, traditional 3D GPR imaging requires dense spatial sampling along regular grids, which is time-consuming and often impractical, especially in complex environments with obstacles or accessibility issues. In this paper, we introduce a novel method that leverages sparse recovery techniques to enhance 3D GPR imaging from reduced spatial measurements collected along arbitrary scanning paths. By exploiting the inherent sparsity of subsurface targets, we employ the Dantzig Selector with cross-validation to accurately reconstruct target locations from spatially random-sampled GPR data. The reconstructed data is then processed using the Back-Projection Algorithm (BPA) to generate high-resolution 3D images. We validate our method through simulations, demonstrating that our approach not only improves imaging quality but also significantly reduces data acquisition time and storage requirements. Performance analysis under various noise levels and sampling densities highlights the robustness and practicality of our method for flexible scanning paths in 3D GPR applications. This work contributes to making GPR surveys more efficient and effective, particularly in scenarios where traditional dense sampling is challenging.