A new technique for estimating the coarse-scale profile of a moderately rough interface between air and a homogeneous dielectric halfspace is presented. The proposed approach is based on space-time sparsely sampled reflected field observations and uses a quasi-ray Gaussian beam fast-forward model, coupled with a compact parameterization of the surface profile in terms of B-splines, from which the profile estimation problem is posed as a nonlinear optimization problem. Numerical experiments are presented to assess accuracy, reliability, and computational efficiency. The proposed approach finds applications in adaptive schemes for rough surface underground imaging of shallowly buried targets via ultra wide-band ground penetrating radars.