Ground-penetrating radar (GPR) full-waveform inversion (FWI) is an emerging near-surface high-resolution imaging technology that has been widely used in GPR 2-D imaging to better quantitatively evaluate the permittivity and conductivity of the subsurface. However, the 2-D imaging method limits the applicability and accuracy of FWI for the 3-D object cases. In this letter, we develop a 3-D FWI algorithm involving permittivity and conductivity for GPR in the frequency domain. The method employs the edge-based finite element method to solve the forward problem and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to solve the inverse problem, which avoids the calculation of the Hessian matrix. In particular, by using the parameter scaling and scaling factor, it is convenient to carry out the simultaneous inversion of permittivity and conductivity with high efficiency. In addition, a modified total variation regularization scheme is utilized for ensuring the stability of the inversion, as well as identifying the abnormal body boundary more effectively. As a demonstration, a synthetic 3-D model experiment is presented to test the proposed algorithm. The results show that the proposed inversion strategy can accurately reconstruct the permittivity structure together with the conductivity distribution from the 3-D on-ground GPR data.

Full waveform inversion (FWI) of ground-penetrating radar (GPR) data is becoming a promising technique to facilitate the interpretation of surface-GPR data and the mapping of the subsurface. However, more general FWIs still require a sufficient amount of RAM memory, and it is difficult to produce an accurate and representative reconstruction result due to a large amount of the Hessian matrix calculations and singular value decomposition (SVD). In this article, we developed a novel full-waveform approach of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm for surface-GPR data that is based on a quasi-Newton framework and the total variation (TV) regularization. The proposed approach uses an L-BFGS algorithm and combines a scale-transformation regularization technique to mitigate the ill-posed problem of inversion, which can impose a biparameter preinformation constraint to ensure the stability of inversion, and adaptive regularization weights are applied to improve the convergence efficiency of inversion. To demonstrate the novelty and effectiveness of the proposed scheme, we tested our FWI algorithm using synthetic data and in-site field data. In the testing, we focus on analyzing the influence of different aspects of the FWI results, including different scale factors, regularization weights, inversion strategies, acquisition configurations, initial models, and the noisy data set. In particular, the FWI experiment is performed to demonstrate the applicability of the proposed algorithm. The results show that the proposed algorithm can effectively reconstruct the biparameter near the subsurface with high accuracy, which makes our approach very attractive for attribute analysis applications and makes the surface-GPR FWI commercially viable.

The high-fidelity attenuation of random ground penetrating radar (GPR) noise is important for enhancing the signal-noise ratio (SNR). In this paper, a novel network structure for convolutional denoising autoencoders (CDAEs) was proposed to effectively resolve various problems in the noise attenuation process, including overfitting, the size of the local receptive field, and representational bottlenecks and vanishing gradients in deep learning; this approach also significantly improves the noise attenuation performance. We described the noise attenuation process of conventional CDAEs, and then presented the output feature map of each convolutional layer to analyze the role of convolutional layers and their impacts on GPR data. Furthermore, we focused on the problems of overfitting, the local receptive field size, and the occurrence of representational bottlenecks and vanishing gradients in deep learning. Subsequently, a network structure optimization strategy, including a dropout regularization layer, an atrous convolution layer, and a residual-connection structure, was proposed, namely convolutional denoising autoencoders with network structure optimization (CDAEsNSO), comprising an intermediate version, called atrous-dropout CDAEs (AD-CDAEs), and a final version, called residual-connection CDAEs (ResCDAEs), all of which effectively improve the performance of conventional CDAEs. Finally, CDAEsNSO was applied to attenuate noise for the H-beam model, tunnel lining model, and field pipeline data, confirming that the algorithm adapts well to both synthetic and field data. The experiments verified that CDAEsNSO not only effectively attenuates strong Gaussian noise, Gaussian spike impulse noise, and mixed noise, but it also causes less damage to the original waveform data and maintains high-fidelity information.