Crosshole GPR Full Waveform Inversion with a Deep Iterative Unfolding Network

Summary Cross-hole ground penetrating radar (GPR) full waveform inversion (FWI) is a powerful technique for high-resolution imaging of subsurface properties. However, the traditional FWI method presents challenges such as falling into local minima and high computational costs. Data-driven deep learning is considered a potential solution to the FWI problem, while its ability is limited in the cross-hole GPR FWI due to the lack of sufficient labeled samples. To alleviate these difficulties, we propose ADMM-Unet, a deep iterative unfolding network that integrates physics-driven principles into deep learning, for cross-hole GPR FWI. ADMM-Unet does not rely on source wavelet estimation by using a convolutional objective function, and it decomposes the inversion problem into three subproblems based on the Alternating Direction Method of Multipliers (ADMM) algorithm. The gradient used to update the permittivity model is calculated by automatic differentiation, and a soft-threshold-based convolutional neural network is designed to learn the proximal operator in the regularization subproblem. Experimental results show that the proposed method significantly improves inversion accuracy and computational efficiency compared to traditional FWI methods with L1 or L2 regularization.