Many tensor-based data completion methods aim to solve image and video in-painting problems. But, all methods were only developed for a single dataset. In most of real applications, we can usually obtain more than one dataset to reflect one phenomenon, and all the datasets are mutually related in some sense. Thus one question raised whether such the relationship can improve the performance of data completion or not? In the paper, we proposed a novel and efficient method by exploiting the relationship among datasets for multi-video data completion. Numerical results show that the proposed method significantly improve the performance of video in-painting, particularly in the case of very high missing percentage.
In many different field, multi-data analysis or group analysis was also deeply discussed @cite_0 @cite_2 @cite_4 . But the majority of methods focus on common and distinctive component extraction. In this paper, we do not care latent features in each dataset. Thus we can reduce the complexity of algorithms compared to tensor decomposition based method like @cite_5 @cite_8 . A multi-matrix completion method Convex Collective Matrix Factorization (cCMF) was proposed in @cite_4 . Compare to cCMF, The proposed method in this paper can be considered as an extension of cCMF into tensor problem.
@cite_4 @cite_8 @cite_0 @cite_2 @cite_5
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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-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4]. 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-D and 4- D (color) video data completion and de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, the notion of multilinear rank and a related tensor nuclear norm was proposed in [11] to characterize informational and structural complexity of multilinear data. We first show that videos with linear camera motion can be represented more efficiently using t-SVD compared to the approaches based on vectorizing or flattening of the tensors. Since efficiency in representation implies efficiency in recovery, we outline a tensor nuclear norm penalized algorithm for video completion from missing entries. Application of the proposed algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. We also consider the problem of tensor robust Principal Component Analysis (PCA) for de-noising 3-D video data from sparse random corruptions. We show superior performance of our method compared to the matrix robust PCA adapted to this setting as proposed in [4]. CANDECOMP PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance. In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for tensor decomposition. In contrast to popular existing tensor decomposition techniques such as higher-order SVD (HOSVD), t-SVD has optimality properties similar to the truncated SVD for matrices. Based on t-SVD, we first construct novel tensor-rank like measures to characterize informational and structural complexity of multilinear data. Following that we outline a complexity penalized algorithm for tensor completion from missing entries. As an application, 3-D and 4-D (color) video data compression and recovery are considered. We show that videos with linear camera motion can be represented more efficiently using t-SVD compared to traditional approaches based on vectorizing or flattening of the tensors. Application of the proposed tensor completion algorithm for video recovery from missing entries is shown to yield a superior performance over existing methods. In conclusion we point out several research directions and implications to online prediction of multilinear data.