Back projection algorithm based on linear estimation of refraction point position for subsurface imaging in layered scenes

Back projection (BP) algorithm is widely used for ground penetrating radar (GPR) imaging of layered scenes. Considering the inevitable refraction phenomenon in the layered scenes, the BP algorithm necessitates repeatedly solving quartic equations all over the imaging scene to determine the positions of refraction points. However, the existing algorithms calculate the quartic equation of the refraction point through iterative approximations, especially when the relative permittivity of the scene gradually increases. These algorithms rely on the manual setting of the iteration threshold and are time consuming. Therefore, this paper proposes a BP algorithm based on linear estimation of refraction point position (LERP) for the layered scene with decreasing permittivity. We propose a two-step LERP algorithm that rewrites the quartic equation of the refraction point and directly estimates the refraction point position. The LERP algorithm consists of the coarse estimation inspired by the scene features and the precise estimation guaranteed by the quartic equation. The LERP algorithm reduces the quartic equation to a linear algebraic form. Following this, the LERP-based BP algorithm promotes efficient imaging in the case of decreasing permittivity. Comprehensive experiments verify that the proposed LERP algorithm meets the resolution requirements of GPR exploration. Compared with the existing algorithms, the proposed algorithm avoids manually setting iteration thresholds, and improves the efficiency of estimating refraction point positions and thus the BP algorithm.