Traditional ground-penetrating radar (GPR) data inversion leverages iterative algorithms that suffer from high computation costs and low accuracy when applied to complex subsurface scenarios. Existing deep learning-based methods focus on the ideal homogeneous subsurface environments and ignore the interference due to clutters and noise in real-world heterogeneous environments. To address these issues, a two-stage deep neural network (DNN), called DMRF-UNet, is proposed to reconstruct the permittivity distributions of subsurface objects from GPR B-scans under heterogeneous soil conditions. In the first stage, a U-shape DNN with first multi-receptive-field convolution (MRF-UNet1) is built to remove the clutters due to inhomogeneity of the heterogeneous soil. Then, the denoised B-scan from MRF-UNet1 is combined with the noisy B-scan to be inputted to the DNN in the second multi-receptive-field convolution (MRF-UNet2). MRF-UNet2 learns the inverse mapping relationship and reconstructs the permittivity distribution of subsurface objects. To avoid information loss, an end-to-end training method combining the loss functions of two stages is introduced. A wide range of subsurface heterogeneous scenarios and B-scans are generated to evaluate the inversion performance. The test results in the numerical experiment and the real measurement show that the proposed network reconstructs the permittivities, shapes, sizes, and locations of subsurface objects with high accuracy. The comparison with existing methods demonstrates the superiority of the proposed methodology for the inversion under heterogeneous soil conditions.

The reconstruction of the 3D permittivity map from ground-penetrating radar (GPR) data is of great importance for mapping subsurface environments and inspecting underground structural integrity. Traditional iterative 3D reconstruction algorithms suffer from strong non-linearity, ill-posedness, and high computational cost. To tackle these issues, a 3D deep learning scheme, called 3DInvNet, is proposed to reconstruct 3D permittivity maps from GPR C-scans. The proposed scheme leverages a prior 3D convolutional neural network with a feature attention mechanism to suppress the noise in the C-scans due to subsurface heterogeneous soil environments. Then a 3D U-shaped encoder-decoder network with multi-scale feature aggregation modules is designed to establish the optimal inverse mapping from the denoised C-scans to 3D permittivity maps. Furthermore, a three-step separate learning strategy is employed to pre-train and fine-tune the networks. The proposed scheme is applied to numerical simulation as well as real measurement data. The quantitative and qualitative results show the networks’ capability, generalizability, and robustness in denoising GPR C-scans and reconstructing 3D permittivity maps of subsurface objects.

VoxHenry, a fast Fourier transform (FFT)-accelerated integral-equation-based simulator for extracting frequency-dependent inductances and resistances of structures discretized by voxels, is presented. VoxHenry shares many features with the popular inductance extractor, FastHenry. Just like FastHenry, VoxHenry solves a combination of the electric volume integral equation and the current continuity equation, but with three distinctions that make VoxHenry suitable and extremely efficient for analyzing voxelized geometries: 1) it leverages a carefully selected set of piecewise-constant and piecewise-linear basis functions; 2) it exploits FFTs to accelerate the matrix-vector multiplications during the iterative solution of system of equations; and 3) it employs a sparse preconditioner to ensure the rapid convergence of iterative solution. VoxHenry is capable of accurately computing frequency-dependent inductances and resistances of arbitrarily shaped and large-scale structures on a desktop computer. The accuracy, efficiency, and applicability of VoxHenry are demonstrated through inductance analysis of various structures, including square and circular coils as well as arrays of RF inductors (situated over ground planes).

A compact ultra-wideband dual-polarized Vivaldi antenna is proposed for full polarimetric ground-penetrating radar (GPR) applications. A shared-aperture configuration comprising four Vivaldi elements for orthogonal polarizations is designed to reduce the low-end operating frequency and improve the port isolation with a compact antenna size. The directivity of the antenna is enhanced by the oblique position of the radiators and the implementation of a square loop reflector. Experimental results demonstrate that the antenna has very good impedance matching, port isolation, and dual-polarized radiation performance, with low dispersion characteristics across band of interest from 0.4 GHz to 3.0 GHz. GPR measurements with the designed antenna show that the antenna maintains good detection capability even for objects buried in a highly conductive soil.

VoxCap, a fast Fourier transform (FFT)-accelerated and Tucker-enhanced integral equation simulator for capacitance extraction of voxelized structures, is proposed. The VoxCap solves the surface integral equations (SIEs) for the conductor and dielectric surfaces with three key attributes that make the VoxCap highly CPU and memory-efficient for the capacitance extraction of the voxelized structures: 1) VoxCap exploits the FFTs for accelerating the matrix-vector multiplications during the iterative solution of the linear system of equations arising due to the discretization of SIEs; 2) during the iterative solution, VoxCap uses a highly effective and memory-efficient preconditioner that reduces the number of iterations significantly; and 3) VoxCap employs the Tucker decompositions to compress the block Toeplitz and circulant tensors, requiring the largest memory in the simulator. By doing so, it reduces the memory requirement of these tensors from hundreds of gigabytes to a few megabytes and the CPU time required to obtain the Toeplitz tensors from tens of minutes (even hours) to a few seconds for very large-scale problems. VoxCap is capable of accurately computing capacitance of arbitrarily shaped and large-scale voxelized structures on a desktop computer. VoxCap's accuracy, efficiency, and capability are demonstrated through capacitance extraction of various large-scale structures, including the parallel meander lines discretized by more than a hundred million panels and analyzed on a commodity desktop computer.

A butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the $O(N\log ^{2}N)$ construction cost of the HOD-BF-compressed system matrix and $O(N^{1.5}\log N)$ inversion cost for the preconditioner, where $N$ is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a $\mathcal {H}$ matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.