Low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention in recent years. However, low-rank assumption is not sufficient for recovering visual data, such as color and 3D images, under extremely high missing ratio. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm to perform tensor completion, which is particularly powerful for visual data. The proposed method gains the significant advantages due to the integration of smooth PARAFAC decomposition (PD) for an incomplete tensor and efficient model selection for minimizing tensor rank, which is thus termed as "Smooth Parafac tensor Completion" (SPC). To impose the smoothness constraints, we employed two strategies including total variation (SPC-TV) and squared variation (SPC-SV), and provide the corresponding algorithms for model learning. The extensive experimental evaluations on both synthetic and real-world visual data illustrated the significant improvements, in terms of prediction performance and efficiency, as compared with many state-of-the-art tensor completion methods.
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