This paper proposes a new variational model for deblurring low-resolution images, a.k.a. single image nonparametric blind super-resolution. In specific, a type of new adaptive heavy-tailed image priors are presented incorporating both the model discriminativeness and effectiveness of salient edge pursuit for accurate and reliable blur kernel estimation. With the assistance of appropriate non-blind super-resolution approaches, nonparametric blind super-resolution can be cast as a regularized functional minimization problem. An efficient numerical algorithm is derived by harnessing the alternating direction method of multipliers as well as the conjugate gradient method, with which alternatingly iterative estimations for kernel and image are finally implemented in a multi-scale manner. Numerous experiments are conducted along with comparisons made among the proposed approach and two recent state-of-the-art ones, demonstrating that the proposed approach is able to better deal with low-resolution images which are blurred by various possible kernels, e.g., Gaussian shaped kernels of varying sizes, ellipse-shaped kernels of varying orientations, curvilinear kernels of varying trajectories.