Depth maps, characterizing per-pixel physical distance between objects in a 3D scene and a capturing camera, can now be readily acquired using inexpensive active sensors such as Microsoft Kinect. However, the acquired depth maps are often corrupted due to surface reflection or sensor noise. In this paper, we build on two previously developed works in the image denoising literature to restore single depth maps-i.e., to jointly exploit local smoothness and nonlocal self-similarity of a depth map. Specifically, we propose to first cluster similar patches in a depth image and compute an average patch, from which we deduce a graph describing correlations among adjacent pixels. Then we transform similar patches to the same graph-based transform (GBT) domain, where the GBT basis vectors are learned from the derived correlation graph. Finally, we perform an iterative thresholding procedure in the GBT domain to enforce group sparsity. Experimental results show that for single depth maps corrupted with additive white Gaussian noise (AWGN), our proposed NLGBT denoising algorithm can outperform state-of-the-art image denoising methods such as BM3D by up to 2.37dB in terms of PSNR.