Refined GPR signal reconstruction using a unified approach of reverse time migration and projection onto convex sets

SUMMARY Absence of traces tends to reduce the quality and reliability of ground penetrating radar (GPR) data due to equipment, sensor coverage and acquisition limitations. This is a significant limitation to full waveform inversion and reverse time migration (RTM) advanced imaging techniques, which rely on dense and continuous data. To address this challenge, we propose an effective interpolation method using the Projection onto Convex Sets (POCS) algorithm, originally developed for seismic data reconstruction. The algorithm is formulated in a compressed sensing framework, taking advantage of Fourier sparsity and iterative thresholding in the time domain to iteratively update spectral coefficients during reconstruction. We compare its performance on synthetic and real GPR data with various percentages of missing data. Results indicate that the POCS algorithm, in addition to reconstructing missing traces at high precision, significantly improves subsequent RTM imaging structural resolution. We also compare POCS with conventional Kriging and a deep learning-based interpolation model (DL-Net) to benchmark its performance. The proposed method achieves superior reconstruction quality and stability, particularly under high sparsity conditions. This study highlights the practical potential of POCS in enhancing GPR image fidelity and interpretation under real-world acquisition limitations.