An Iterative l1-Regularized Least Absolute Deviation Algorithm for Robust GPR Imaging

We present an l(1)-regularized least absolute deviation (l(1)-LAD) algorithm for estimating subsurface reflection coefficients from ground penetrating radar (GPR) measurements. The l(1)-regularization incorporates the known sparsity of the reflection coefficients for typical scenes, while the LAD criteria provides robustness against potential outliers/spikes in the data. The majorize-minimize (MM) principle is used to solve the l(1)-LAD optimization problem and the resulting iterative algorithm is straightforward to implement and computationally efficient with judicious data processing and/or parallelization. The l(1)-LAD algorithm is amenable to parallelization because the MM procedure decouples the estimation of the reflection coefficients. The robustness and effectiveness of the proposed l(1)-LAD algorithm is validated using a I-D timeseries and simulated GPR dataset.