Robust balancing scheme-based approach for tensor completion

Gao, Shangqi; Fan, Qing‐Hua

doi:10.1016/j.neucom.2018.11.033

Cited by 4 publications

(3 citation statements)

References 24 publications

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“…In this section, we compare the proposed algorithm with tensor completion algorithms including simple low-rank tensor completion via tensor train (SiLRTCTT), 6 smooth low-rank tensor tree completion (STTC), 38 tensor ring low-rank factors (TRLRF), 15 tensor ring weighted optimization (TRWOPT), 14 tensor ring completion by alternating least square method (TRALS), 13 low-rank tensor completion by parallel matrix factorization based on balancing scheme (BS-TMac), 39 robust low-rank tensor completion via transformed tensor nuclear norm with total variation regularization based on DCT (TNTV (DCT)) 7 or based on the given data (TNTV (Data)) 7,40 and tensor robust principal component analysis (TRPCA). 17 All the experiments are performed under Windows 10 and MATLAB R2021b running on a laptop (Intel(R) Core(TM) i7, @ 2.80 GHz, 16.0 GB RAM).…”

Section: Environment Parameters and Measurementsmentioning

confidence: 99%

An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

Chen,

Huang

2023

Numerical Linear Algebra App

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Robust low‐rank tensor completion plays an important role in multidimensional data analysis against different degradations, such as sparse noise, and missing entries, and has a variety of applications in image processing and computer vision. In this paper, an optimization model for low‐rank tensor completion problems is proposed and a block coordinate descent algorithm is developed to solve this model. It is shown that for one of the subproblems, the closed‐form solution exists and for the other, a Riemannian conjugate gradient algorithm is used. In particular, when all elements are known, that is, no missing values, the block coordinate descent is simplified in the sense that both subproblems have closed‐form solutions. The convergence analysis is established without requiring the latter subproblem to be solved exactly. Numerical experiments illustrate that the proposed model with the algorithm is feasible and effective.

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Section: Environment Parameters and Measurementsmentioning

confidence: 99%

An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

Chen,

Huang

2023

Numerical Linear Algebra App

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“…Real data often have high intrinsic correlations, which are described as low‐rank properties [38–46]. The low‐rank tensor reconstruction problem can be expressed as follows:

$$\begin{equation} \mathop {\arg \min }\limits_\mathcal{R} rank\left( \mathcal{R} \right) s.t{.

…”

Section: Related Workmentioning

confidence: 99%

“…Real data often have high intrinsic correlations, which are described as low-rank properties [38][39][40][41][42][43][44][45][46]. The low-rank tensor reconstruction problem can be expressed as follows:…”

Section: Low-rank Tensor Reconstructionmentioning

confidence: 99%

Salt‐and‐pepper denoising method for colour images based on tensor low‐rank prior and implicit regularization

Zhang

Wang

et al. 2022

IET Image Processing

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Most of the information obtained by humans comes from colour images. However, saltand-pepper noise (SPN) during signal acquisition, encoding, transmission, and decoding easily interferes with the quality of colour images. Most existing SPN denoising methods decompose a colour image into three independent matrices according to the colour channel and then recover each channel signal independently, ignoring the strong data correlation between channels. In addition, most existing SPN denoising methods apply only a single model-driven or data-driven approach and fail to take the advantages of their combination fully. Therefore, we first regard a colour image contaminated by SPN as the sum of an SPN tensor and a tensor with missing data. In this manner, we transform the denoising problem into a low-rank tensor reconstruction problem. We then introduce a model-driven-based parallel matrix factorization low-rank tensor reconstruction algorithm and a data-driven-based FFDNet denoising network to restore the colour image better. The proposed method not only enhances the similarity of the colour image channels but also explores the deep prior of the colour image to capture the image details. Finally, the proposed method is compared with some advanced denoising methods. The results show that the proposed method achieves a competitive denoising performance.

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Iterative tensor eigen rank minimization for low-rank tensor completion

Liu

Tian

et al. 2022

Information Sciences

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Robust balancing scheme-based approach for tensor completion

Cited by 4 publications

References 24 publications

An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

An iterative algorithm for low‐rank tensor completion problem with sparse noise and missing values

Salt‐and‐pepper denoising method for colour images based on tensor low‐rank prior and implicit regularization

Iterative tensor eigen rank minimization for low-rank tensor completion

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