Constrained Low-Tubal-Rank Tensor Recovery for Hyperspectral Images Mixed Noise Removal by Bilateral Random Projections

Zhang, Hao; Zhao, Xi-Le; Jiang, Tai-Xiang; Ng, Michael K.

doi:10.1109/igarss.2019.8899257

Cited by 2 publications

(3 citation statements)

References 15 publications

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“…2 that the recovery results by both DTNN and random t-SVD (RTSVD) methods are presented on video data Flight. These two methods are typical representatives of the transform-based TNN methods [34][35][36][37][38][39][40][41][42] and fast TNN-based methods [43][44][45][46][47]. The results indicate that DTNN provides superior restoration accuracy, but at the cost of higher computational complexity, while RTSVD offers lower computational cost but less impressive recovery result.…”

Section: A Proposed Ls2t2nn Modelmentioning

confidence: 99%

“…To address the challenge computational issue, many fast algorithms were developed [43][44][45][46][47]. Zhang et al [43] proposed a random t-SVD to solve this issue.…”

mentioning

confidence: 99%

“…They constructed a semiorthogonal projection using a random tensor to project a largescale tensor into a small-scale tensor, so that the SVD can be calculated on the small-scale tensor to reduce computational cost. Zhang et al [44] designed a fast algorithm by bilateral random projections, which are utilized to constrain the tubal rank of the intrinsic tensor. Wang et al [45] employed the random projection technique and the power of the block Krylov iteration to accurate frequent directions algorithm.…”

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confidence: 99%

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Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery

Liu,

Leng,

Zhao

et al. 2024

IEEE Trans. Circuits Syst. Video Technol.

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Recently, transform-based tensor nuclear norm (TNN) methods have received increasing attention as a powerful tool for multi-dimensional visual data (color images, videos, and multispectral images, etc.) recovery. Especially, the redundant transform-based TNN achieves satisfactory recovery results, where the redundant transform along spectral mode can remarkably enhance the low-rankness of tensors. However, it suffers from expensive computational cost induced by the redundant transform. In this paper, we propose a learnable spatial-spectral transform-based TNN model for multi-dimensional visual data recovery, which not only enjoys better low-rankness capability but also allows us to design fast algorithms accompanying it. More specifically, we first project the large-scale original tensor to the small-scale intrinsic tensor via the learnable semiorthogonal transforms along the spatial modes. Here, the semiorthogonal transforms, serving as the key building block, can boost the spatial low-rankness and lead to a small-scale problem, which paves the way for designing fast algorithms. Secondly, to further boost the low-rankness, we apply the learnable redundant transform along the spectral mode to the small-scale intrinsic tensor. To tackle the proposed model, we apply an efficient proximal alternating minimization-based algorithm, which enjoys a theoretical convergence guarantee. Extensive experimental results on real-world data (color images, videos, and multispectral images) demonstrate that the proposed method outperforms state-of-the-art competitors in terms of evaluation metrics and running time.

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Section: A Proposed Ls2t2nn Modelmentioning

confidence: 99%

“…To address the challenge computational issue, many fast algorithms were developed [43][44][45][46][47]. Zhang et al [43] proposed a random t-SVD to solve this issue.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery

Liu,

Leng,

Zhao

et al. 2024

IEEE Trans. Circuits Syst. Video Technol.

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Adaptive singular value shrinkage estimate for low rank tensor denoising

Tao

2022

Random Matrices: Theory Appl.

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Recently, tensors are widely used to represent higher-order data with internal spatial or temporal relations, e.g. images, videos, hyperspectral images (HSIs). While the true signals are usually corrupted by noises, it is of interest to study tensor recovery problems. To this end, many models have been established based on tensor decompositions. Traditional tensor decomposition models, such as the CP and Tucker factorization, treat every mode of tensors equally. However, in many real applications, some modes of the data act differently from the other modes, e.g. channel mode of images, time mode of videos, band mode of HSIs. The recently proposed model called t-SVD aims to tackle such problems. In this paper, we focus on tensor denoising problems. Specifically, in order to obtain low-rank estimators of true signals, we propose to use different shrinkage functions to shrink the tensor singular values based on the t-SVD. We derive Stein’s unbiased risk estimate (SURE) of the proposed model and develop adaptive SURE-based tuning parameter selection procedure, which is totally data-driven and simultaneous with the estimation process. The whole modeling procedure requires only one round of t-SVD. To demonstrate our model, we conduct experiments on simulation data, images, videos and HSIs. The results show that the proposed SURE approximates the true risk function accurately. Moreover, the proposed model selection procedure picks good tuning parameters out. We show the superiority of our model by comparing with state-of-the-art denoising models. The experiments manifest that our model outperforms in both quantitative metrics (e.g. RSE, PSNR) and visualizing results.

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Constrained Low-Tubal-Rank Tensor Recovery for Hyperspectral Images Mixed Noise Removal by Bilateral Random Projections

Cited by 2 publications

References 15 publications

Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery

Learnable Spatial-Spectral Transform-Based Tensor Nuclear Norm for Multi-Dimensional Visual Data Recovery

Adaptive singular value shrinkage estimate for low rank tensor denoising

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