Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation

Ding, Meng; Huang, Ting‐Zhu; Ji, Teng-Yu; Zhao, Xi-Le; Yang, Jing‐Hua

doi:10.1007/s10915-019-01044-8

Cited by 74 publications

(36 citation statements)

References 31 publications

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“…Based on its multilinear algebraic properties, a tensor can take full advantage of its structures to provide better understanding and higher accuracy of the multidimensional data. In many real‐world applications, tensor datasets are often corrupted and/or incomplete owing to various unpredictable or unavoidable situations . It motivated us to perform tensor completion and robust tensor completion for multidimensional data processing.…”

Section: Introductionmentioning

confidence: 99%

Robust tensor completion using transformed tensor singular value decomposition

Song

Zhang

2020

Numerical Linear Algebra App

142

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In this article, we study robust tensor completion by using transformed tensor singular value decomposition (SVD), which employs unitary transform matrices instead of discrete Fourier transform matrix that is used in the traditional tensor SVD. The main motivation is that a lower tubal rank tensor can be obtained by using other unitary transform matrices than that by using discrete Fourier transform matrix. This would be more effective for robust tensor completion. Experimental results for hyperspectral, video and face datasets have shown that the recovery performance for the robust tensor completion problem by using transformed tensor SVD is better in peak signal-to-noise ratio than that by using Fourier transform and other robust tensor completion methods. K E Y W O R D Slow-rank, robust tensor completion, sparsity, transformed tensor singular value decomposition, unitary transform matrix

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Section: Introductionmentioning

confidence: 99%

Robust tensor completion using transformed tensor singular value decomposition

Song

Zhang

2020

Numerical Linear Algebra App

142

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“…Furthermore, He et al [22] integrated a unified framework to simultaneously consider the spectral and spatial low-rankness, where the nuclear norm to explore the low-rank property and the total variation (TV) regularization to capture smooth information of HSI. However, the 3-D HSI will be reshaped into 2-D if using the matrix-based approaches, which destroys the spatial correlation [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Zeng

Huang

Chen

et al. 2021

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Since the facility restrictions and weather conditions, hyperspectral image (HSI) is generally seriously polluted by a variety of noises. Recently, the method based on block term decomposition with rank-(L, L, 1) (BTD) has attracted wide attention in HSI mixed noise removal. BTD factorizes thirdorder HSI data into the sum of a series of component tensors, where each of the component tensors is represented by the outer product of a rank-L matrix ArB T r and a column vector cr. BTD has clear physical interpretation because its latent factors ArB T r and cr can be interpreted abundance map and spectral signature respectively. The essential uniqueness of BTD is under the lowrank assumption of ArB T r . However, the low-rank assumption is not always held in real scenarios. The BTD-based method usually sets L to full rank to achieve satisfactory results. In this paper, we suggest a novel model based on nonlocal block term decomposition (NLBTD) for HSI mixed noise removal. More specifically, for each grouped similar image block, BTD is introduced to capture nonlocal self-similarity and global spectral lowrankness, the unidirectional total variation (TV) is introduced to preserve local spectral smoothness. By faithfully exploring nonlocal self-similarity, global spectral low-rankness, and local spectral smoothness, the proposed method is expected to produce promising results with guarantee the essential uniqueness of BTD. To tackle the resulting model, we design an efficient algorithm based on the proximal alternating minimization with the theoretical guarantees. Extensive numerical experiments in HSI mixed noise removal demonstrate that the proposed NLBTD method achieves satisfactory performance compared with stateof-the-art methods.

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“…When processing color images, in order to better capture the local low-rank characteristic of the image, it converts the third-order tensor of the image data into an Nthorder tensor (N > 3) through kat augmentation (KA) [27], and then minimizes the TT rank of the tensor to recover the damaged image. A large number of studies [27][28][29] have shown that, compared with other rank minimization methods, the image recovered by the TT rank contains more detailed information.…”

Section: Introductionmentioning

confidence: 99%

Low-rank tensor completion via combined Tucker and Tensor Train for color image recovery

et al. 2021

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In recent years, low-rank tensor completion has been widely used in color image recovery. Tensor Train (TT), as a balanced tensor rank minimization method, has achieved good results in actual image recovery because of its ability to capture the hidden information of images. When processing the third-order tensor data of a color image, TT transforms it into a higherorder tensor through kat augmentation to exploit the local feature of the tensor effectively. However, this method actually destroys the original structure of the tensor, which leads to insufficient access to the global structure information. Therefore, the algorithm performs poorly when processing images with a significant amount of missing information. Aiming at this problem, a new tensor completion model is proposed, which combines Tucker rank and Tensor Train rank. Among them, Tucker is used to obtain the global structure information, and Tensor Train is used to capture the local hidden information.To tackle the proposed model, we develop an efficient alternating direction method based algorithm. The numerical experiments using various tensor data show the effectiveness of the model.

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Low-Rank Tensor Completion Using Matrix Factorization Based on Tensor Train Rank and Total Variation

Cited by 74 publications

References 31 publications

Robust tensor completion using transformed tensor singular value decomposition

Robust tensor completion using transformed tensor singular value decomposition

Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Low-rank tensor completion via combined Tucker and Tensor Train for color image recovery

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