Reflectivity-Consistent Sparse Blind Deconvolution for Denoising and Calibration of Multichannel GPR Volume Images

Vehicle-mounted multichannel ground penetrating radar (MC-GPR) is a revolutionary technology that facilitates the acquisition of volume images by arranging multiple antennas; however, its images are highly affected by noise due to different antenna characteristics. This study proposes reflectivity-consistent sparse blind deconvolution (RC-SBD) for appropriate denoising of ground penetrating radar (GPR) volume images. RC-SBD interprets the observed waveform as the convolution of the emitted wavelets and reflectivity, plus stationary clutter such as reflections from the vehicle itself. The method obtains denoised reflectivity by estimating the wavelets and clutter. The key feature of RC-SBD is that it extends the existing SBD method to 3-D, and introduces an assumption of reflectivity smoothness in the horizontal direction, expressed by the total variation (TV) regularization term. The estimation is formulated as a minimization problem involving $\ell _{2}$ and $\ell _{1}$ norms and is optimized using the Split–Bregman algorithm. Trade-off hyperparameters of the objective function are optimized via Bayesian optimization, maximizing the kurtosis of the calibrated volume image. Validation with synthetic data demonstrates accurate wavelet estimation and significant denoising of the volume image. Real-world data application further reveals considerable improvements in the channel-depth cross section, providing a clear visualization of structures like rebar and steel plates. Notably, the calibrated image remains stable across diverse datasets, including earthwork and bridge sections, showcasing the versatility and reliability of the proposed methodology.