Low CP Rank and Tucker Rank Tensor Completion for Estimating Missing Components in Image Data

Liu, Yipeng; Zhang, Long; Huang, Huyan; Zhu, Ce

doi:10.1109/tcsvt.2019.2901311

Cited by 79 publications

(30 citation statements)

References 57 publications

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“…In this section, we compare the proposed method to other state-of-the-art methods on three visual-data sets: (i) A hyperspectral image (HSI) 1 of size 200 × 200 × 80, which records the area of urban landscape; (ii) The Train-video 2 which consists of 80 color frames of size 72 × 128 × 3, presented by a tensor of size 72×128×3×80; (iii) The AT&T ORL 3 face data set which consists of 10 different images of size 32 × 32 for each of 40 distinct subjects, presented by a tensor of size 32 × 32 × 10 × 40. Since reshaping the visual data into high-order tensor significantly improve the performance of the TT/TR-based methods (i.e.…”

Section: Visual Data Inpaintingmentioning

confidence: 99%

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding schemes. To overcome this drawback, a new latent nuclear norm equipped with a more balanced unfolding scheme is defined for low-rank regularizer. Moreover, the new latent nuclear norm together with the Frank-Wolfe (FW) algorithm is developed as an efficient completion method by utilizing the sparsity structure of observed tensor. Specifically, both FW linear subproblem and line search only need to access the observed entries, by which we can instead maintain the sparse tensors and a set of small basis matrices during iteration. Most operations are based on sparse tensors, and the closed-form solution of FW linear subproblem can be obtained from rank-one SVD. We theoretically analyze the space-complexity and time-complexity of the proposed method, and show that it is much more efficient over other norm-based completion methods for higher-order tensors. Extensive experimental results of visual-data inpainting demonstrate that the proposed method is able to achieve state-of-the-art performance at smaller costs of time and space, which is very meaningful for the memory-limited equipment in practical applications. INDEX TERMS Tensor completion, tensor ring decomposition, tensor ring rank, latent nuclear norm, image/video inpainting.

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Section: Visual Data Inpaintingmentioning

confidence: 99%

An Efficient Tensor Completion Method Via New Latent Nuclear Norm

Sun

Qiu

et al. 2020

IEEE Access

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“…ADMM and APG are two most popular first-order approaches for solving problem (3). ADMM separates the objective function via additionally introduced variables, which may results in tedious parameter setting and slow convergence.…”

Section: B General Solution With Apgmentioning

confidence: 99%

“…On that basis, finding a low-rank solution to an optimization problem, e.g., matrix completion (MC) or subspace clustering (SC), has attracted a great deal of attention over the last decade. Concrete applications, where low-rank modeling of X is relevant, can be found in scene reconstruction [2], video inpainting [3], background subtraction [4], or video matting [5], among many others.…”

Section: Introductionmentioning

confidence: 99%

Efficient Implementation of Truncated Reweighting Low-Rank Matrix Approximation

Zheng

Qin

Zhou

et al. 2020

IEEE Trans. Ind. Inf.

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The weighted nuclear norm minimization and truncated nuclear norm minimization are two well-known low-rank constraint for visual applications. By integrating their advantages into a unified formulation, we find a better weighting strategy, namely truncated reweighting norm minimization (TRNM), which provides better approximation to the target rank for some specific task. Albeit nonconvex and truncated, we prove that TRNM is equivalent to certain weighted quadratic programming problems, whose global optimum can be accessed by the newly presented reweighting singular value thresholding operator. More importantly, we design a computationally efficient optimization algorithm, namely momentum update and rank propagation (MURP), for the general TRNM regularized problems. The individual advantages of MURP include: (1) reducing iterations through non-monotonic search, and (2) mitigating computational cost by reducing the size of target matrix. Furthermore, the descent property and convergence of MURP are proven. Finally, two practical models, i.e., MCTRNM and SCTRNM, are presented for visual applications. Extensive experimental results show that our methods achieve better performance, both qualitatively and quantitatively, compared with several state-of-the-art algorithms.

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“…For example, CANDECOMP/PARAFAC (CP) rank [6,32,63] minimizes the sparsity of tensors over bases of rank-1 outer products; Tucker rank [31,45,48] focuses on the low-rankness of unfolding matrices along different modes; tubal rank [15,25,30,60] promotes the tubal sparsity under the tensor singular value decomposition (t-SVD), by treating third-order tensors as linear operators on matrices; tensor train (TT) rank [2,38] and its extension tensor ring (TR) rank [13,21] capture the global correlation among tensor entries using matrix product states. Considering that each type of tensor rank encodes a specific correlated data structure, recent studies attempt to integrate the insights delivered by different low-rank tensor formats, such as joint CP rank and Tucker rank minimization [33], weighted low-rank tensor recovery (WLRTR) [10], and Kronecker-basis-representation (KBR)based tensor low-rankness measure [54].…”

Section: Introductionmentioning

confidence: 99%