This paper describes a new algorithm for depth image super resolution and denoising using a single depth image as input. A robust coupled dictionary learning method with locality coordinate constraints is introduced to reconstruct the corresponding high resolution depth map. The local constraints effectively reduce the prediction uncertainty and prevent the dictionary from over-fitting. We also incorporate an adaptively regularized shock filter to simultaneously reduce the jagged noise and sharpen the edges. Furthermore, a joint reconstruction and smoothing framework is proposed with an L0 gradient smooth constraint, making the reconstruction more robust to noise. Experimental results demonstrate the effectiveness of our proposed algorithm compared to previously reported methods.