Sparsity-Promoted Blind Deconvolution of Ground-Penetrating Radar (GPR) Data

Abstract

Over the past decades, numerous efforts have been attempted to enhance the temporal resolution and accuracy of subsurface ground-penetrating radar (GPR) data by means of blind deconvolution techniques. The fact that most of the source wavelets that are utilized in practical GPR exploration are nonminimum phase presents some challenges for the blind deconvolution of GPR data. This letter extends the classical minimum entropy deconvolution strategy and forms a general-purpose framework of the blind deconvolution of GPR data, which formulates the blind deconvolution of GPR data as a sparsity-promoted optimization problem with a scale-invariant regularizer. Another contribution of this letter is that an alternating iterative method is explored to solve the derived nonconvex optimization problem, where the constraint of max <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> |r(t)| = 1 is introduced to avoid trapping into some local minimums. Selected examples are presented to demonstrate the accuracy and robustness of the proposed methodology. Primary results show that by applying such approach to the GPR data, we obtain images with significantly enhanced temporal resolution compared with the results of existing blind deconvolution schemes.