Recovering low‐rank tensor from limited coefficients in any ortho‐normal basis using tensor‐singular value decomposition

Ma, Shuli; Ai, Jianhang; Du, Heng; Fang, Liping; Mei, Wenbo

doi:10.1049/sil2.12017

Cited by 5 publications

(7 citation statements)

References 45 publications

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“…[17] gives an overview of tensor-based models and methods for multi-sensor signal processing, such as the Tucker decomposition [27,47], the canonical polyadic decomposition [48], the tensor-train decomposition (TTD), the structured TTD and so on. Ma et al [16] used tensor singular value decomposition(t-SVD) to learn a lowrank tensor from limited coefficients in any ortho-normal basis. Liu et al [49] proposed a proximal operator for the approximation of tensor nuclear norms based on tensor-train rank-1 decomposition with the SVD.…”

Section: Related Workmentioning

confidence: 99%

“…Ma et al. [16] used tensor singular value decomposition(t‐SVD) to learn a low‐rank tensor from limited coefficients in any ortho‐normal basis. Liu et al.…”

Section: Related Workmentioning

confidence: 99%

“…Particularly, the matrix or 2-D data can be regarded as a special data of tensor [5,6] (the 2-D methods only suitable for 2-D images). Tensor-based methods have well performance in many application fields, such as image analysis [5,7,8], recommendation system [9,10], wireless spectrogram generation [11], seismic signals processing [12], computer vision [13], Hyperspectral image analysis [14][15][16], sensor signal processing [17] and so on. Recently, many tensor-based dimensionality reduction (TDR) algorithms have been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Tensor dimensionality reduction via mode product and HSIC

Niu

2021

IET Image Processing

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Tensor dimensionality reduction (TDR) is a hot research topic in machine learning, which learns data representations by preserving the original data structure while avoiding convert samples into vectors and solving the problem of the curse of dimensionality of tensor data. In the work, a novel TDR approach based on mode product and Hilbert-Schmidt Independence criterion (HSIC) is proposed. The contributions of authors' work is described as following: (1) HSIC measures the statistical correlation of two random variables. However, instead of measuring the statistical correlation of two random variables directly, HSIC first transforms the two random variables into two reproducing kernel Hilbert spaces (RKHSs), and then measures the statistical correlation of transformed random variables by using Hilbert-Schmidt operators between the two RKHSs. The exploitation of RKHS increases the flexibility and applicability of HSIC. Although HSIC is widely used in machine learning, the authors have not seen its application to dimensionality reduction (DR)(except for authors' previous work). (2) A novel HSIC-based TDR approach is proposed, which first applies HSIC to capture statistical information of tensor data set for DR. The authors give the mathematical derivation of HSIC for tensor data and establish a framework of TDR based on HSIC, named HSIC-TDR for short, which aims to improve the DR results of tensor by exploring and preserving the statistical information of original data set. (3) Furthermore, to solve the out-of-sample problem, the authors learn an explicit expression between the dimensionality-reduced tensors and the higher-dimensional tensors by introducing mode product to HSIC-TDR. The experimental results between the proposed method and other state-of-the-art algorithm on various datasets demonstrate the well performance of the proposed method.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Related Workmentioning

confidence: 99%

“…Ma et al. [16] used tensor singular value decomposition(t‐SVD) to learn a low‐rank tensor from limited coefficients in any ortho‐normal basis. Liu et al.…”

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Tensor dimensionality reduction via mode product and HSIC

Niu

2021

IET Image Processing

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“…With the progress in the research and development of tensor decomposition tools in the field of mathematics, such as t-SVD, TT decomposition, etc. [10,11,17], related image or video optimization applications based on a low-rank tensor are also being developed [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Review of Matrix Rank Constraint Model for Impulse Interference Image Inpainting

Ma,

Li,

Chu

et al. 2024

Electronics

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Camera failure or loss of storage components in imaging equipment may result in the loss of important image information or random pulse noise interference. The low-rank prior is one of the most important priors in image optimization processing. This paper reviews and compares some low-rank constraint models for image matrices. Firstly, an overview of image-inpainting models based on nuclear norm, truncated nuclear norm, weighted nuclear norm, and matrix-factorization-based F norm is presented, and corresponding optimization iterative algorithms are provided. Then, we use different image matrix low-order constraint models to recover satellite images from three types of pulse interference and provide our experimental visual and numerical results. Finally, it can be concluded that the method based on the weighted nuclear norm can achieve the best image restoration effect. The F norm method based on matrix factorization has the shortest computational time and can be used for large-scale low-rank matrix calculations. Compared with nuclear norm-based methods, weighted nuclear norm-based methods and truncated nuclear norm-based methods can significantly improve repair performance.

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“…The square root of the covariance matrix is used for iteration to ensure the positive semidefiniteness of the covariance matrix. In [22,23], singular value decomposition (SVD) is proposed to replace square root decomposition to better ensure the stability of numerical calculations. In order to ensure the positive determination of the error covariance matrix, SVD is applied to our algorithm.…”

mentioning

confidence: 99%

Robust strong tracking unscented Kalman filter for non‐linear systems with unknown inputs

Liu

Guan

Jiang

et al. 2022

IET Signal Processing

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This paper proposes a state estimation approach ‘robust strong tracking unscented Kalman filter with unknown inputs’ that can be applied to non‐linear systems with unknown inputs. Specifically, the non‐linear state and measurement equations are linearised by statistical linearisation. Then, the estimation equation of the unknown input is derived based on the weighted least squares method. The multiple suboptimal fading factor is introduced into a priori error covariance matrix to improve the tracking ability for the inaccuracy of the system model and the abrupt change of state variables caused by unknown inputs. Finally, based on the unbiased minimum variance estimation, the unbiased state estimation and the error covariance matrix are derived. Singular value decomposition is performed on the error covariance matrix to improve the stability of the algorithm. Simulated results validate the effectiveness of the proposed method.

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Recovering low‐rank tensor from limited coefficients in any ortho‐normal basis using tensor‐singular value decomposition

Cited by 5 publications

References 45 publications

Tensor dimensionality reduction via mode product and HSIC

Tensor dimensionality reduction via mode product and HSIC

Review of Matrix Rank Constraint Model for Impulse Interference Image Inpainting

Robust strong tracking unscented Kalman filter for non‐linear systems with unknown inputs

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