An Iterative Parameter-Free MAP Algorithm With an Application to Forward Looking GPR Imaging

Ground-penetrating radar (GPR) has been used in a number of applications including the detection of land-mines and improvised explosive devices. Most existing algorithms for forward looking GPR image reconstruction require that a hyperparameter or regularization parameter be chosen by the user. Selecting these parameters in an optimal fashion is a challenging problem that, in theory, can be addressed using cross validation and the L-curve method. Unfortunately, these hyperparameter selection methods are time consuming and not well suited for real-time applications. In this paper, we propose a hyperparameter-free algorithm that follows from a maximum a posteriori (MAP) formulation where the prior probability density function is obtained by the so-called "integrate-out" approach. First, we model the reflection coefficients as statistically independent random variables that are identically distributed and Laplacian with parameter, lambda. Then, we analytically integrate out the parameter, lambda, and optimize the resulting MAP objective function using the majorize-minimize optimization technique and soft-thresholding operator. We tested the algorithm using synthetic and real experimental data, and compared the results subjectively and objectively with the results obtained from well-known algorithms. Although the evaluation is not an exhaustive study, it demonstrates the feasibility of the proposed algorithm.