Recently, consumer depth cameras have gained significant popularity due to their affordable cost. However, the limited resolution and quality of the depth map generated by these cameras are still problems for several applications. In this paper, we propose a new algorithm for depth image super resolution using a single depth image as input. We reconstruct the corresponding high resolution depth map through a robust coupled dictionary learning algorithm with local coordinate constraints. The local constraints remove the prediction uncertainty and prevent the dictionary from over-fitting. We also incorporate an adaptively regularized Shock filter to simultaneously reduce the noise and sharpen the edges. Experimental results demonstrate the effectiveness of our proposed algorithm compared to previously reported methods.