Tensor Completion via Generalized Tensor Tubal Rank Minimization Using General Unfolding

Sun, Weize; Chen, Yuan; So, Hing Cheung

doi:10.1109/lsp.2018.2819892

Cited by 20 publications

(26 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The iGTKD approach proposed in this article, on the other hand, does not have such problems. Furthermore, the definition of the improved tensor multi-rank, which is not shown in [34], is clearly defined in this article. It is worthy to note that the CGTNN and ACGTNN approaches in [34] are minimising the improved tensor tubal-rank, while the tensor completion approach to be proposed in next section is in fact minimises the improved tensor multi-rank.…”

Section: Definition 262mentioning

confidence: 99%

“…The data X can also be sampled randomly under a predefined observation percentage to get the data tensor M Ω with missing elements, and the tensor recovery methods can be applied for the recovery of the original data as c X , Finally the recovered image can be calculated as b I . The peak SNR (PSNR) and structural similarity (SSIM) [49] Here we follow and modify the idea in [33,34] to set the patterns transferring the original 2-D M 1 � M 2 data to 3-D K � J � L structure under the following rules: The L refers to the most detail information, and is set to be a small value. While the K � J should be as square as possible or follow a similar shape of M 1 � M 2 .…”

Section: Sar Imagingmentioning

confidence: 99%

“…Note that for the t-SVD approach, we fold the fourth dimension into the third one for t-SVD. The patterns for CGTNN and ACGTNN follows those in [34] To verify the advantage of using multiple patterns instead of single pattern, we evaluate the proposed method under the four cases: using only one of the three patterns P 1 , P 2 and P 3 , and using all of them, under 30% observation percentage. The PSNR results are shown in Table 4 and the recovered first and last frames of the video are shown in Figure 13.…”

Section: Sar Imagingmentioning

confidence: 99%

See 2 more Smart Citations

Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Sun

Zhang

Zhao

2021

IET Signal Processing

View full text Add to dashboard Cite

The authors address the problem of tensor completion from limited samplings. An improved generalized tubal Kronecker decomposition is first proposed to reveal the tensor structure of the targeted data, and the improved generalized tensor tubal-rank and multi-rank are also introduced. The tensor completion problem is then formulated as the improved multi-rank minimisation problem. Instead of using the singular value decomposition(SVD), this work proposes an alternating optimisation method to update all of the subspaces of the data tensor for the recovery process, and thus it is computationally inexpensive. A rank-decreasing method is derived to reveal the tensor rank in order to avoid the troublesome user defined hyper-parameter selection. Experiments are carried out on both the synthetic data and the real datasets, and it is shown that the proposed approach can get a better performance than the state-of-the-art approaches with moderate computational complexity.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.

show abstract

Section: Definition 262mentioning

confidence: 99%

Section: Sar Imagingmentioning

confidence: 99%

Section: Sar Imagingmentioning

confidence: 99%

See 1 more Smart Citation

Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Sun

Zhang

Zhao

2021

IET Signal Processing

View full text Add to dashboard Cite

show abstract

“…Recently, the low-tubal-rank model [16,25] has shown better performance than traditional tensor low-rank models in many tensor recover tasks such as image/video inpainting/denoising/ sensing [2,25,26], moving object detection [27], multi-view learning [28], seismic data completion [29], WiFi fingerprint [30], MRI imaging [16], point cloud data inpainting [31], and so on. The tubal rank is a new complexity measure of tensor defined through the framework of tensor singular value decomposition (t-SVD) [32,33]. At the core of existing low-tubal-rank models is the tubal nuclear norm (TNN) which is a convex surrogate for the tubal rank.…”

Section: Introductionmentioning

confidence: 99%

Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms

Fang

Wei

Zhang³

2019

Sensors

View full text Add to dashboard Cite

The rapid development of sensor technology gives rise to the emergence of huge amounts of tensor (i.e., multi-dimensional array) data. For various reasons such as sensor failures and communication loss, the tensor data may be corrupted by not only small noises but also gross corruptions. This paper studies the Stable Tensor Principal Component Pursuit (STPCP) which aims to recover a tensor from its corrupted observations. Specifically, we propose a STPCP model based on the recently proposed tubal nuclear norm (TNN) which has shown superior performance in comparison with other tensor nuclear norms. Theoretically, we rigorously prove that under tensor incoherence conditions, the underlying tensor and the sparse corruption tensor can be stably recovered. Algorithmically, we first develop an ADMM algorithm and then accelerate it by designing a new algorithm based on orthogonal tensor factorization. The superiority and efficiency of the proposed algorithms is demonstrated through experiments on both synthetic and real data sets.

show abstract

“…Recently, a novel low-rank tensor model called the low-tubal-rank model was proposed [22,30]. The core of it is to model the 3D data as a tensor that has low tubal-rank [31], which is defined through a new tensor singular value decomposition (t-SVD) [1,32]. It has been successfully used in modeling multi-way real-world data, such as color images [6], videos [33], seismic data [34], WiFi fingerprint [35], MRI imaging [22], traffic volume data [36], etc.…”

Section: Introductionmentioning

confidence: 99%

Tensor Completion Based on Triple Tubal Nuclear Norm

et al. 2018

View full text Add to dashboard Cite

Many tasks in computer vision suffer from missing values in tensor data, i.e., multi-way data array. The recently proposed tensor tubal nuclear norm (TNN) has shown superiority in imputing missing values in 3D visual data, like color images and videos. However, by interpreting in a circulant way, TNN only exploits tube (often carrying temporal/channel information) redundancy in a circulant way while preserving the row and column (often carrying spatial information) relationship. In this paper, a new tensor norm named the triple tubal nuclear norm (TriTNN) is proposed to simultaneously exploit tube, row and column redundancy in a circulant way by using a weighted sum of three TNNs. Thus, more spatial-temporal information can be mined. Further, a TriTNN-based tensor completion model with an ADMM solver is developed. Experiments on color images, videos and LiDAR datasets show the superiority of the proposed TriTNN against state-of-the-art nuclear norm-based tensor norms.

show abstract

Tensor Completion via Generalized Tensor Tubal Rank Minimization Using General Unfolding

Cited by 20 publications

References 27 publications

Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Rank revealing‐based tensor completion using improved generalized tensor multi‐rank minimization

Stable Tensor Principal Component Pursuit: Error Bounds and Efficient Algorithms

Tensor Completion Based on Triple Tubal Nuclear Norm

Contact Info

Product

Resources

About