Tensor completion using total variation and low-rank matrix factorization

Ji, Teng-Yu; Huang, Ting‐Zhu; Zhao, Xi-Le; Ma, Tianhui; Liu, Gang

doi:10.1016/j.ins.2015.07.049

Cited by 161 publications

(76 citation statements)

References 34 publications

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“…It appears to be natural to directly extend low-rank matrix factorization methods to the low-rank tensor factorization problem. Based on this definition, Ji et al [48] further proposed a nonconvex approach. However, these methods involved the singular value decomposition (SVD) of Y (n) , which is time-consuming.…”

Section: Tensor Tucker Factorization Modelmentioning

confidence: 99%

A Low-Rank Tensor Factorization Using Implicit Similarity in Trust Relationships

Ma¹,

Wang²,

Qin³

2020

Symmetry

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Low-rank tensor factorization can not only mine the implicit relationships between data but also fill in the missing data when working with complex data. Compared with the traditional collaborative filtering (CF) algorithm, the changes are essentially proposed, from traditional matrix analysis to three-dimensional spatial analysis. Based on low-rank tensor factorization, this paper proposes a recommendation model that comprehensively considers local information and global information, in other words, combining the similarity between trust users and low-rank tensor factorization. First, the similarity between trusted users is measured to capture local information between users by trusting similar preferences of users when selecting items. Then, the users’ similarity is integrated into the tensor, and the low-rank tensor factorization is used to better maintain and describe the internal structure of the data to obtain global information. Furthermore, based on the idea of the alternating least squares method, the conjugate gradient (CG) optimization algorithm for the model of this paper is designed. The local and global information is used to generate the optimal expected result in an iterative process. Finally, we conducted a large number of comparative experiments on the Ciao dataset and the FilmTrust dataset. Experimental results show that the algorithm has less precision loss under the data set with lower density. Thus, not only can a perfect compromise between accuracy and coverage be achieved, but also the computational complexity can be reduced to meet the need for real-time results.

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Section: Tensor Tucker Factorization Modelmentioning

confidence: 99%

A Low-Rank Tensor Factorization Using Implicit Similarity in Trust Relationships

Ma¹,

Wang²,

Qin³

2020

Symmetry

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“…The symmetric alternating direction method with multipliers (symmetric ADMM) is an acceleration method of ADMM, which can be used to solve the constraint optimization formulation in image processing [34][35][36][37][38][39][40][41][42][43].…”

Section: Symmetric Admmmentioning

confidence: 99%

“…Many optimization methods can be applied to solve the proposed formulation (P2), such as the split Bregman method, alternating direction method with multipliers [35][36][37][38][39][40]42,43,49,50]. Here, we employ symmetric ADMM to solve (P2) due to its simplicity and efficiency [34].…”

Section: Optimization Algorithmmentioning

confidence: 99%

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

et al. 2018

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Hyperspectral unmixing, aiming to estimate the fractional abundances of pure spectral signatures in each mixed pixel, has attracted considerable attention in analyzing hyperspectral images. Plenty of sparse unmixing methods have been proposed in the literature that achieved promising performance. However, many of these methods overlook the latent geometrical structure of the hyperspectral data which limit their performance to some extent. To address this issue, a double reweighted sparse and graph regularized unmixing method is proposed in this paper. Specifically, a graph regularizer is employed to capture the correlation information between abundance vectors, which makes use of the property that similar pixels in a spectral neighborhood have higher probability to share similar abundances. In this way, the latent geometrical structure of the hyperspectral data can be transferred to the abundance space. In addition, a double weighted sparse regularizer is used to enhance the sparsity of endmembers and the fractional abundance maps, where one weight is introduced to promote the sparsity of endmembers as a hyperspectral image typically contains fewer endmembers compared to the overcomplete spectral library and the other weight is exploited to improve the sparsity of the abundance matrix. The weights of the double weighted sparse regularizer used for the next iteration are adaptively computed from the current abundance matrix. The experimental results on synthetic and real hyperspectral data demonstrate the superiority of our method compared with some state-of-the-art approaches.

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“…Nowadays, the TV regularization is widely extended to other fields, such as nature image restoration [42,43] and tensor completion [44]. Comparing with Tikhonov-like regularization, TV regularization has a better ability to effectively preserve sharp edges and promote piecewise smooth objects.…”

Section: Tv Regularizationmentioning

confidence: 99%

Stripe noise removal of remote sensing images by total variation regularization and group sparsity constraint

et al. 2017

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Remote sensing images have been used in many fields, such as urban planning, military, and environment monitoring, but corruption by stripe noise limits its subsequent applications. Most existing stripe noise removal (destriping) methods aim to directly estimate the clear images from the stripe images without considering the intrinsic properties of stripe noise, which causes the image structure destroyed. In this paper, we propose a new destriping method from the perspective of image decomposition, which takes the intrinsic properties of stripe noise and image characteristics into full consideration. The proposed method integrates the unidirectional total variation (TV) regularization, group sparsity regularization, and TV regularization together in an image decomposition framework. The first two terms are utilized to exploit the stripe noise properties by implementing statistical analysis, and the TV regularization is adopted to explore the spatial piecewise smooth structure of stripe-free image. Moreover, an efficient alternating minimization scheme is designed to solve the proposed model. Extensive experiments on simulated and real data demonstrate that our method outperforms several existing state-of-the-art destriping methods in terms of both quantitative and qualitative assessments.

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Tensor completion using total variation and low-rank matrix factorization

Cited by 161 publications

References 34 publications

A Low-Rank Tensor Factorization Using Implicit Similarity in Trust Relationships

A Low-Rank Tensor Factorization Using Implicit Similarity in Trust Relationships

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

Stripe noise removal of remote sensing images by total variation regularization and group sparsity constraint

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