Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

Cai, Shuting; Luo, Qilun; Yang, Ming; Li, Wen; Xiao, Mingqing

doi:10.3390/app9071411

Cited by 28 publications

(6 citation statements)

References 39 publications

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“…as suggested in Reference [89][90][91][92]. e resulting convergence curves are as shown in Figure 1, from which we can see that the RSEs of the proposed algorithm for all images decrease with the iteration number and then reach at a constant after a few iterations.…”

Section: Experimental Convergence Performancementioning

confidence: 55%

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation

Likassa

Xia²,

Gotu

2022

Scientific Programming

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In this study, an effective robust PCA is developed for joint image alignment and recovery via L 2,1 norms and affine transformations. To alleviate the potential impacts of outliers, heavy sparse noises, occlusions, and illuminations, the L 2,1 norms along with affine transformations are taken into consideration. The determination of the parameters involved and the updating affine transformations is arranged in the form of a constrained convex optimization problem. To reduce the computation load, we also further decompose the error as sparse error and Gaussian noise; additionally, the alternating direction method of multipliers (ADMM) is considered to develop a new set of recursive equations to update the optimization parameters and the affine transformations iterative. The convergence of the derived updating equation is explained as well. Conducted simulations illustrate that the new method is superior to the baseline works in terms of precision on some public databases.

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Section: Experimental Convergence Performancementioning

confidence: 55%

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation

Likassa

Xia²,

Gotu

2022

Scientific Programming

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“…In order to illustrate the effect of rank selection on image restoration, we selected the Washington DC Mall dataset (SR = 10%) to carry out image restoration simulation experiments with different r, where r is taken from [20,20,20] to [40,40,40], and the results are shown in Figure 8a,b. It can be seen that the overall trend of MPSNR and MSSIM increases with the increase in r. When r > [25,25,25], the curve begins to decline.…”

Section: Parameter Analysismentioning

confidence: 99%

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Liu

et al. 2020

Remote Sensing

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Low-rank tensors have received more attention in hyperspectral image (HSI) recovery. Minimizing the tensor nuclear norm, as a low-rank approximation method, often leads to modeling bias. To achieve an unbiased approximation and improve the robustness, this paper develops a non-convex relaxation approach for low-rank tensor approximation. Firstly, a non-convex approximation of tensor nuclear norm (NCTNN) is introduced to the low-rank tensor completion. Secondly, a non-convex tensor robust principal component analysis (NCTRPCA) method is proposed, which aims at exactly recovering a low-rank tensor corrupted by mixed-noise. The two proposed models are solved efficiently by the alternating direction method of multipliers (ADMM). Three HSI datasets are employed to exhibit the superiority of the proposed model over the low rank penalization method in terms of accuracy and robustness.

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“…Using the kernel norm, the TRPCA problem is solved with convex programming. It is often used in image noise reduction and image restoration research [30][31][32][33]. However, no study has reported the use of the TRPCA algorithm for detecting multi-component mixtures.…”

Section: Introductionmentioning

confidence: 99%

Near-Infrared Spectral Characteristic Extraction and Qualitative Analysis Method for Complex Multi-Component Mixtures Based on TRPCA-SVM

Zhang

Tuo

Zhai

et al. 2022

Sensors

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Quality identification of multi-component mixtures is essential for production process control. Artificial sensory evaluation is a conventional quality evaluation method of multi-component mixture, which is easily affected by human subjective factors, and its results are inaccurate and unstable. This study developed a near-infrared (NIR) spectral characteristic extraction method based on a three-dimensional analysis space and establishes a high-accuracy qualitative identification model. First, the Norris derivative filtering algorithm was used in the pre-processing of the NIR spectrum to obtain a smooth main absorption peak. Then, the third-order tensor robust principal component analysis (TRPCA) algorithm was used for characteristic extraction, which effectively reduced the dimensionality of the raw NIR spectral data. Finally, on this basis, a qualitative identification model based on support vector machines (SVM) was constructed, and the classification accuracy reached 98.94%. Therefore, it is possible to develop a non-destructive, rapid qualitative detection system based on NIR spectroscopy to mine the subtle differences between classes and to use low-dimensional characteristic wavebands to detect the quality of complex multi-component mixtures. This method can be a key component of automatic quality control in the production of multi-component products.

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Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

Cited by 28 publications

References 39 publications

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Near-Infrared Spectral Characteristic Extraction and Qualitative Analysis Method for Complex Multi-Component Mixtures Based on TRPCA-SVM

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Tensor Robust Principal Component Analysis via Non-Convex Low Rank Approximation

Cited by 28 publications

References 39 publications

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the L 2,1 Norms and Affine Transformation

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the L 2,1 Norms and Affine Transformation

Hyperspectral Image Recovery Using Non-Convex Low-Rank Tensor Approximation

Near-Infrared Spectral Characteristic Extraction and Qualitative Analysis Method for Complex Multi-Component Mixtures Based on TRPCA-SVM

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An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation

An Efficient New Robust PCA Method for Joint Image Alignment and Reconstruction via the $L_{2,1}$ Norms and Affine Transformation