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

Abstract

<p> Vehicle-mounted multichannel ground penetrating radar (MC-GPR) facilitates acquisition of volume images of subsurface structures, but inconsistencies arise due to different transmitted wavelets from each antenna. This paper introduces a methodology, Reflectivity-Consistent Sparse Blind Deconvolution (RC-SBD), that estimates transmitted wavelets and stationary clutter for each antenna, thereby calibrating GPR volume images. Previous Sparse Blind Deconvolution was achieved by alternating minimization, producing a single transmitted wavelet and sparse ground reflectivity. RC-SBD utilizes an assumption of subsurface reflectivity smoothness in the horizontal direction, expressed via a total variation regularization term. This allows a wavelet to be derived for each channel. Stationary clutter variables, such as reflection from the vehicle itself and direct waves, are integrated into the model for simultaneous estimation. The objective function incorporates several ℓ2 and ℓ1 regularization terms and is solved using the Split Bregman algorithm augmented by a gradient method. Hyperparameters are determined through Bayesian optimization, aiming to maximize kurtosis of the frequency domain calibrated volume image. The proposed methodology was validated with synthetic data, demonstrating accurate wavelets estimation and significant denoising of volume image. Real-world data application revealed substantial enhancements in the channel depth cross section, visualizing responses of structures such as rebar and steel plates. Furthermore, calibrated image remained stable across diverse datasets, including earthwork and bridge sections, indicating the estimates’ versatility. </p>