High-accuracy reconstruction of missing ground-penetrating radar signals based on projection onto convex sets in the curvelet domain

Influence by the acquisition environments and instrument performance, missing signals and destructed channels are inevitable in measured ground-penetrating radar (GPR) profiles. They can cause event discontinuity of reflected and diffracted waves generated by targets, severely impairing the accuracy and resolution of subsequent processing and imaging. Hence, by combining the projection onto convex sets (POCS) algorithm extensively used in image processing with the curvelet transform exhibiting high sparsity, this study proposed a high-accuracy reconstruction method for missing GPR signals based on curvelet-domain POCS. Building on the compressive sensing theory, the objective function for missing signal reconstruction based on discrete curvelet transform was established, and the time-domain iterative equation for reconstructing missing GPR signals was derived in detail using POCS. The curvelet transform coefficients were updated using linear and exponential iterative threshold models for high-accuracy reconstruction of missing signals in the time domain. The reconstruction accuracy of missing GPR signals was quantitatively evaluated using mean absolute errors (MAEs), signal-to-noise ratios (SNRs), and peak SNRs (PSNRs). The reconstruction experiments of simulated and measured GPR signals show that POCS can effectively reconstruct the missing signals in GPR profiles. Contrasting with the POCS of the linear threshold model, the POCS of the exponential threshold model yielded higher reconstruction accuracy. In the exponential threshold model, compared to frequency-domain POCS, curvelet-domain POCS exhibited smaller reconstruction errors and weaker longitudinal artifact energy during the reconstruction of continuous multi-channel missing signals in GPR profiles, and higher applicability to the reconstruction of missing signals in complex structural models. In contrast to the frequency-domain POCS of both linear and exponential threshold models and the curvelet-domain POCS of the linear threshold model, the curvelet-domain POCS reconstruction method of the exponential threshold model manifested higher reconstruction accuracy, average absolute errors reduced by 45%‒99%, and SNRs and PSNRs enhanced by 1‒20 dB, providing high-quality GPR signals for subsequent processing and interpretation.