A Deblurring Algorithm for Impulse Based Forward-Looking Ground Penetrating Radar Images Reconstructed Using the Delay-and-Sum Algorithm

Presently, the delay-and-sum (DAS) algorithm, also known as the backprojection algorithm, is the most popular way to reconstruct impulse based forward-looking ground penetrating radar (FLGPR) images. Nevertheless, it is widely known that the DAS algorithm has poor clutter rejection capability and generates FLGPR images with low resolution. The advantage of the DAS algorithm is its computational speed and ability to reconstruct scatterers within a scene-of-interest that are sufficiently spaced. In this paper, we propose a deblurring algorithm that is based on a model for DAS images whereby the known system matrix depends on the transmitted signal, and the propagation delays associated with the transmitted and backscattered signals. Using a DAS image as the data, an improved FLGPR image is obtained by estimating the true reflection coefficients via a popular estimation method known as the least absolute shrinkage and selection operator (LASSO). The objective function that results from LASSO is minimized using the majorization-minimization optimization technique. We refer to the proposed algorithm as the deblurring DAS (D-DAS) algorithm. Using synthetic data, we provide subjective results where the D-DAS algorithm significantly outperformed the standard DAS algorithm.