Ground penetrating radar (GPR) subsurface sensing is a promising nondestructive evaluation (NDE) technique for inspecting and surveying underground utilities in complex urban environments, as well as for monitoring other key infrastructure such as bridges and railroads. A challenge of such technique lies on image formation from the recorded GPR data. In this work, a fast back projection algorithm (BPA) for three-dimensional GPR image construction is explored. The BPA is a time-domain migration method that has been effectively used in GPR image formation. However, most of the studies in the literature apply a computationally intensive BPA to a two-dimensional dataset under the assumption that an in-plane scattering occurs underneath the GPR antennas. This assumption is not precise for 3D GPR image formation as the GPR radiation scatters in multiple directions as it reaches the ground. In this study, a generalized form for an approximation to determine the scattering point in an air-coupled GPR system is developed which considerably reduces the required computations and can accurately localize the scattering point position. The algorithm is evaluated by applications on GPR data synthesized using GprMax, a finite-difference time domain (FDTD) simulator.
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