Integrating short-time linear canonical transform and joint space-time-frequency analysis for advanced representation of subsurface information in ground penetrating radar.

Ground Penetrating Radar (GPR) is a widely used non-destructive sensing technique for subsurface exploration. The Short-Time Fourier Transform (STFT) and other classical time-frequency analysis methods are commonly employed to enhance the signal-to-noise ratio and highlight subsurface anomalies. However, their performance is fundamentally constrained by the time-bandwidth product theorem, limiting their ability to effectively analyze time-varying, non-smooth signals. To overcome these limitations, we propose the Short-Time Linear Canonical Transform (STLCT) as a more adaptive and flexible alternative for GPR signal processing. STLCT offers improved time-frequency localization and enhanced resolution when dealing with non-stationary signals. We establish its theoretical foundation, including key properties and a convolution theorem that ensures computational efficiency. To validate STLCT, we simulate realistic subsurface scenarios using GPRMAX 2.0 and evaluate the method on synthetic and real-world GPR data. The results demonstrate that STLCT consistently outperforms classical methods in terms of adaptability, clarity, and robustness, offering improved signal interpretation in complex environments. These findings suggest STLCT as a robust and practical enhancement to advanced GPR signal processing pipelines.