Ground-penetrating radar (GPR) is used to image and detect subterranean objects, for example, in landmine detection. Although full 3-D inversion of GPR measurements is possible for simple algorithms such as backprojection, it is impractical when using more advanced algorithms that involve l(1)-minimization. Many of the algorithms used for GPR imaging involve the storage, or online generation, of a huge dictionary matrix created from discretizing a high-dimensional nonlinear model. This parametric model includes all the target features that need to be extracted, including 3-D location, object orientation, and target type. As more parameters are added to the model, the dimensionality increases. If uniform sampling is done over high-dimensional parameter space, the size of the dictionary and the complexity of the inversion algorithms rapidly grow, exceeding the capability of real-time processors. This paper shows that strategic structuring of the dictionary, which takes advantage of translational invariance in the model, can reduce the dictionary storage by several orders of magnitude and exploit the fast Fourier transform for fast computation of previously highly impractical, bordering on impossible, 3-D GPR imaging problems.