An Iterative ℓ1-regularized least absolute deviation algorithm for robust GPR Imaging

Abstract

We present an ℓ₁-regularized least absolute deviation (ℓ₁-LAD) algorithm for estimating subsurface reflection coefficients from ground penetrating radar (GPR) measurements. The ℓ₁-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 ℓ₁-LAD optimization problem and the resulting iterative algorithm is straightforward to implement and computationally efficient with judicious data processing and/or parallelization. The ℓ₁-LAD algorithm is amenable to parallelization because the MM procedure decouples the estimation of the reflection coefficients. The robustness and effectiveness of the proposed ℓ₁-LAD algorithm is validated using a 1-D time series and simulated GPR dataset.