In this paper, by observing the intrinsic sparsity of saliency map for the image, we propose a novel nonlocal minimization framework to extract the sparse geometric structure of the saliency maps for the natural images. Specifically, we first propose to use the -nearest neighbors of superpixels to construct a graph in the feature space. The novel -regularized nonlocal minimization model is then developed on the proposed graph to describe the sparsity of saliency maps. Finally, we develop a first order optimization scheme to solve the proposed non-convex and discrete variational problem. Experimental results on four publicly available data sets validate that the proposed approach yields significant improvement compared with state-of-the-art saliency detection methods.