An ℓ1-regularized least-squares deblurring algorithm with an application to GPR imaging

The delay-and-sum (DAS) algorithm is widely used to reconstruct ground penetrating radar (GPR) images because of its simplicity and speed. However the drawback of the DAS algorithm is that it produces images with poor resolution and significant sidelobes. In this paper, we present a method that deblurs the DAS image using the least absolute shrinkage and selection operator (LASSO) without incurring the high computation cost associated with conventional LASSO. In a limited study using simulated data, the proposed deblurring algorithm produces images that are sparse with significantly reduced sidelobes.