Nonconvex 3D array image data recovery and pattern recognition under tensor framework

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

doi:10.1016/j.patcog.2021.108311

Cited by 34 publications

(6 citation statements)

References 30 publications

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“…Over the past two decades, numerous approaches to denoising HSI have been proposed [6,7,8,9,10,11,14,15,16,17,18]. Many of these techniques make use of traditional image denoising methods by treating each spectral band of the HSI as a grayscale image [6] or by considering each pixel across all spectral bands as a signal [7].…”

Section: Introductionmentioning

confidence: 99%

Hyperspectral image restoration based on color superpixel segmentation

Huang,

Peng,

et al. 2023

Stat., optim. inf. comput.

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Hyperspectral images (HSI) are often degraded by various types of noise during the acquisition process, such as Gaussian noise, impulse noise, dead lines and stripes, etc. Recently, there exists a growing attenrion on low-rank matrix/tensor-based methods for HSI data restoration, assuming that the overall data is low-rank. However, the assumption of overall low-rankness often proves inaccurate due to the spatially heterogeneous local similarity characteristics of HSI. Traditional cube-based methods involve dividing the HSI into fixed-size cubes. However, using fixed-size cubes does not provide flexible coverage of locally similar regions at varying scales. Inspired by superpixel segmentation, this paper proposes the Shrink Low-rank Super-tensor (SLRST) approach for HSI recovery. Instead of using fixed-size cubes, SLRST employs a size-adaptive super-tensor. The proposed approach is effectively solved using the Alternating Direction Method of Multipliers (ADMM). Numerical experiments on HSI data verify that the proposed method outperforms other competing methods.

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Section: Introductionmentioning

confidence: 99%

Hyperspectral image restoration based on color superpixel segmentation

Huang,

Peng,

et al. 2023

Stat., optim. inf. comput.

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“…If the index set Ω is the whole set, i.e., no elements are missing, then the model (1) reduces to the Tensor Robust Principal Component Analysis (TRPCA) problem [31]- [39].…”

Section: Introductionmentioning

confidence: 99%

Robust High-Order Tensor Recovery Via Nonconvex Low-Rank Approximation

Qin

Wang

et al. 2022

ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD based low-rank approximation, which suffers from high computational costs when dealing with large-scale tensor data. Moreover, most of them are only applicable to third-order tensors. Against these issues, in this article, two efficient low-rank tensor approximation approaches fusing randomized techniques are first devised under the order-d (d ≥ 3) T-SVD framework. On this basis, we then further investigate the robust highorder tensor completion (RHTC) problem, in which a double nonconvex model along with its corresponding fast optimization algorithms with convergence guarantees are developed. To the best of our knowledge, this is the first study to incorporate the randomized low-rank approximation into the RHTC problem. Empirical studies on large-scale synthetic and real tensor data illustrate that the proposed method outperforms other state-ofthe-art approaches in terms of both computational efficiency and estimated precision.

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“…Yang et al [35] adopt the nonconvex log-determinant to capture the low-rank characteristics of tensor and solve the nonconvex tensor completion problem via the alternating direction method of multipliers (ADMM). In addition, the weighted tensor nuclear norm (WTNN) [36] is exploited for LRTC and similar noncovnex regularizer models can be found in [37]- [40]. Recently, Wang et al [10] extend the nonconvex penalty functions [41], [42] used in low-rank matrix completion to the low-tubal rank tensor recovery, and develop a generalized nonconvex tensor completion technique.…”

Section: Introductionmentioning

confidence: 99%

“…While these LRTC algorithms based on nonconvex surrogates have better recovery performance than TNN based tensor completion methods, most noncovex regularization functions do not have closed-form thresholding operators [10], [33], [40]. This means that iterations are needed to find their thresholding operators, leading to a high computational load.…”

Section: Introductionmentioning

confidence: 99%

Low-Rank Tensor Completion by Approximating the Tensor Average Rank

Wang

Dong

Liu

et al. 2021

2021 IEEE/CVF International Conference on Computer Vision (ICCV)

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To alleviate the bias generated by the ℓ1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

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Nonconvex 3D array image data recovery and pattern recognition under tensor framework

Cited by 34 publications

References 30 publications

Hyperspectral image restoration based on color superpixel segmentation

Hyperspectral image restoration based on color superpixel segmentation

Robust High-Order Tensor Recovery Via Nonconvex Low-Rank Approximation

Low-Rank Tensor Completion by Approximating the Tensor Average Rank

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