An MM-based maximum a posteriori algorithm for GPR image reconstruction

In this paper, we use the maximum a posteriori (MAP) method to develop an algorithm that reconstructs subsurface images from GPR datasets. The prior probability density function we have chosen is novel and enforces sparsity. The negative of the objective function resulting from the MAP method is minimized using a majorize-minimize algorithm. An advantage of the proposed method over the popular L1-regularized least-squares method is that there is a straightforward and computationally efficient way to determine the parameter for the prior distribution. We tested the algorithm on synthetic data and promising results were obtained.