An MM-based algorithm for L1-regularized least squares estimation in GPR image reconstruction

We present a regularized Least-Squares (LS) method for estimating subsurface reflection coefficients from ground penetrating radar (GPR) measurements. The expected sparsity of the reflection coefficients induced via L₁-regularization. The majorize-minimize (MM) framework is used to develop a novel iterative algorithm for solving the L₁-regularized LS problem in a straightforward and effective manner. The proposed L₁-regularized Least-Squares (L₁-LS) algorithm is amenable to parallel implementation since the MM procedure decouples the estimation of the individual reflection coefficients. In order to work toward an extended algorithm that would be suited for real-time implementations, we investigate an online strategy for choosing the regularization parameter. The L₁-LS algorithm is validated using simulated GPR datasets.