In this paper, we propose a novel -regularized optimization framework for image downscaling. The optimization is driven by two -regularized priors. The first prior, gradient-ratio prior, is based on the observation that the number of edges in the downscaled image is approximately inverse square proportional to the downscaling factor. By introducing norm sparsity to the gradient ratio, the downscaled image is able to preserve the most salient edges as well as the visual perception of the original image. The second prior, downsampling prior, is to constrain the downsampling matrix so that pixels of the downscaled image are estimated according to those optimal neighboring pixels. Extensive experiments on the Urban100 and BSDS500 data sets show that the proposed algorithm achieves superior performance over the state-of-the-arts, in terms of both quality and robustness.