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In this paper we propose novel methods for completion (from limited samples)and de-noising of multilinear (tensor) data and as an application consider 3-Dand 4- D (color) video data completion and de-noising. We exploit the recentlyproposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, thenotion of multilinear rank and a related tensor nuclear norm was proposed in[11] to characterize informational and structural complexity of multilineardata. We first show that videos with linear camera motion can be representedmore efficiently using t-SVD compared to the approaches based on vectorizing orflattening of the tensors. Since efficiency in representation impliesefficiency in recovery, we outline a tensor nuclear norm penalized algorithmfor video completion from missing entries. Application of the proposedalgorithm for video recovery from missing entries is shown to yield a superiorperformance over existing methods. We also consider the problem of tensorrobust Principal Component Analysis (PCA) for de-noising 3-D video data fromsparse random corruptions. We show superior performance of our method comparedto the matrix robust PCA adapted to this setting as proposed in [4].

Novel methods for multilinear data completion and de-noising based on tensor-SVD