Adaptive total variation and second-order total variation-based model for low-rank tensor completion

Li, Xin; Huang, Ting‐Zhu; Zhao, Xi-Le; Ji, Teng-Yu; Deng, Liang-Jian

doi:10.1007/s11075-020-00876-y

Cited by 5 publications

(6 citation statements)

References 41 publications

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“…

can be understood as the proportion of low-frequency information each direction contains in the mixed-frequency map. In order to solve problem (10), we use the proximal alternating optimization (PAO) algorithm [ 26 ], which is guaranteed to converge to a critical point under specific circumstances.

where

is the objective function in problem (10);

is a positive model parameter; and variables with the superscript

mean the corresponding variables in the previous iteration.…”

Section: The Proposed Methodsmentioning

confidence: 99%

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TDFusion: When Tensor Decomposition Meets Medical Image Fusion in the Nonsubsampled Shearlet Transform Domain

Zhang

Wang

Sun

et al. 2023

Sensors

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In this paper, a unified optimization model for medical image fusion based on tensor decomposition and the non-subsampled shearlet transform (NSST) is proposed. The model is based on the NSST method and the tensor decomposition method to fuse the high-frequency (HF) and low-frequency (LF) parts of two source images to obtain a mixed-frequency fused image. In general, we integrate low-frequency and high-frequency information from the perspective of tensor decomposition (TD) fusion. Due to the structural differences between the high-frequency and low-frequency representations, potential information loss may occur in the fused images. To address this issue, we introduce a joint static and dynamic guidance (JSDG) technique to complement the HF/LF information. To improve the result of the fused images, we combine the alternating direction method of multipliers (ADMM) algorithm with the gradient descent method for parameter optimization. Finally, the fused images are reconstructed by applying the inverse NSST to the fused high-frequency and low-frequency bands. Extensive experiments confirm the superiority of our proposed TDFusion over other comparison methods.

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“…

where

is the objective function in problem (10);

is a positive model parameter; and variables with the superscript

mean the corresponding variables in the previous iteration.…”

Section: The Proposed Methodsmentioning

confidence: 99%

“…According to [ 19 ], the unique solution of Equation ( 14 ) can be efficiently found by the conjugate gradient (CG) algorithm [ 26 ].…”

Section: The Proposed Methodsmentioning

confidence: 99%

TDFusion: When Tensor Decomposition Meets Medical Image Fusion in the Nonsubsampled Shearlet Transform Domain

Zhang

Wang

Sun

et al. 2023

Sensors

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show abstract

“…The global convergence of the proposed proximal alternate minmization (PAM) algorithm for addressing the proposed model was also proved. Li [11] et al introduced the adaptive total variation and the second-order total variation-based model, which could effectively preserve the local smoothness and alleviate the staircase effect. Some other results can be found in [12,13].…”

Section: Introductionmentioning

confidence: 99%

Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion

et al. 2023

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The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing. For the real-world color images, we proposed a novel model called low-rank quaternion matrix completion (LRQC), which adds total variation and Tikhonov regularization to the factor quaternion matrices to preserve the spatial/temporal smoothness. Moreover, a proximal alternating minimization (PAM) algorithm was proposed to tackle the corresponding optimal problem. Numerical results on color images indicate the advantages of our method.

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“…But second-order TV may lead to over smooth for the recovered images and cannot preserve details and edges well. Therefore, Li et al [18] proposed the parallel matrix factorization model for LRTC based on combing the first-order and second-order regularizations.…”

mentioning

confidence: 99%

“…For the above-mentioned existing methods, some methods only consider the removal of mixed noise without missing entries, such as [43,1,35], which cannot perform well with partial observations. The model proposed in [18] combines the advantages of the first-order TV and the secondorder TV, but it mainly pays attention to cases with missing data and does not consider mixed noise removal. TNTV [26] considers the recovery with missing entries and mixed noises, but using only first-order TV easily leads to undesirable staircase effects.…”

mentioning

confidence: 99%

Enhancing low-rank tensor completion via first-order and second-order total variation regularizations

Gao

Huang

2023

JIMO

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<p style='text-indent:20px;'>Recently, low-rank tensor completion (LRTC) has attracted significant attention since it has been applied in a wide variety of practical areas. Due to the edge-preserving and noise removal properties, total variation (TV) has been extensively used in LRTC problems. However, first-order TV usually causes unexpected staircase effects. In this paper, we focus on the LRTC problem with various degradations, which aims to recover third-order tensors from partial observations corrupted by sparse noise and Gaussian noise. We use the transformed tensor nuclear norm to explore global low-rankness, and the combination of first-order and second-order TV regularizations to alleviate the staircase effects caused by first-order TV. Based on these, we propose a first-order and second-order TV regularizations (FSTV) model. In order to solve the proposed FSTV model, a symmetric Gauss-Seidel based alternating direction method of multipliers is adopted. We also establish its global convergence under very mild conditions. Finally, extensive experiments on different video and multispectral image datasets show the superiority of the proposed method compared with several state-of-the-art methods.</p>

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Adaptive total variation and second-order total variation-based model for low-rank tensor completion

Cited by 5 publications

References 41 publications

TDFusion: When Tensor Decomposition Meets Medical Image Fusion in the Nonsubsampled Shearlet Transform Domain

TDFusion: When Tensor Decomposition Meets Medical Image Fusion in the Nonsubsampled Shearlet Transform Domain

Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion

Enhancing low-rank tensor completion via first-order and second-order total variation regularizations

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