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