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This paper proposes a depth super-resolution method with both transform and spatial domain regularization. In the transform domain regularization, nonlocal correlations are exploited via an auto-regressive model, where each patch is further sparsified with a locally-trained transform to consider intra-patch correlations. In the spatial domain regularization, we propose a multi-directional total variation (MTV) prior to characterize the geometrical structures spatially orientated at arbitrary directions in depth maps. To achieve adaptive regularization, the MTV is weighted for each directional finite difference considering local characteristics of RGB-D data. We develop an accelerated proximal gradient algorithm to solve the proposed model. Quantitative and qualitative evaluations compared with state-of-the-art methods demonstrate that the proposed method achieves superior depth super-resolution performance for …