A Non-Local Tensor Completion Algorithm Based on Weighted Tensor Nuclear Norm
Abstract
:1. Introduction
2. Notations and Preliminaries
2.1. Notations
2.2. Preliminary Definitions and Results
Algorithm 1: t-SVD [35] |
Input: , . Output: , and .
|
Tensor Completion Based on Weighted Tensor Nuclear Norm
Algorithm 2: Tensor completion based on weighted tensor nuclear norm |
Input: Lagrangian multiplier tensor , non-convex surrogate function . Initialize:, , , , , , maxIter = 200. Output: The image after completion. for maxIter do Update by Equation (6); Update by Equation (7); Update Lagrangian multiplier by Equation (8); Compute ; Update weight matrix by Equation (9); if do break; end if end for |
3. Proposed Algorithm Scheme
3.1. Image Pre-Processing
3.2. Patch Match Algorithm
3.3. Wntc Algorithm
Algorithm 3: WNTC Algorithm |
Input: Color image , the set of observed element positions , n, N, number of similar patch T and step s. Output: The color image after completion. fordo ; Pre-process the by triangular-based linear interpolation to obtain ; for each point of do Extract similar tensor by patch match algorithm; Complete by Algorithm 2 to obtain ; end for Regroup the tensor to obtain the recovered tensor ; end for |
Experiments
3.4. Parameter Setting
3.5. Color Image Inpainting
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Sampling Rate | Image | FBCP | HaLRTC | TNN | NL-FBCP | NL-HaLRTC | Song | WNTC | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
RSE | PSNR | RSE | PSNR | RSE | PSNR | RSE | PSNR | RSE | PSNR | RSE | PSNR | RSE | PSNR | ||
0.2 | Lena | 0.200 | 19.26 | 0.396 | 13.86 | 0.131 | 23.04 | 0.099 | 25.29 | 0.115 | 24.42 | 0.077 | 27.43 | 0.076 | 27.55 |
A.ort | 0.136 | 19.33 | 0.208 | 15.79 | 0.100 | 22.00 | 0.085 | 23.44 | 0.099 | 22.40 | 0.070 | 25.01 | 0.069 | 25.18 | |
B.oon | 0.232 | 18.29 | 0.369 | 14.66 | 0.198 | 19.81 | 0.167 | 20.49 | 0.186 | 20.69 | 0.145 | 22.27 | 0.145 | 22.23 | |
B.ara | 0.249 | 18.57 | 0.405 | 14.80 | 0.162 | 22.36 | 0.116 | 25.01 | 0.149 | 23.43 | 0.102 | 26.18 | 0.099 | 26.38 | |
House | 0.163 | 20.17 | 0.327 | 14.53 | 0.101 | 24.42 | 0.071 | 27.31 | 0.101 | 24.68 | 0.066 | 28.03 | 0.061 | 28.61 | |
P.ers | 0.271 | 16.84 | 0.510 | 12.13 | 0.197 | 19.79 | 0.109 | 24.58 | 0.132 | 23.39 | 0.088 | 26.41 | 0.086 | 26.62 | |
S.oat | 0.229 | 17.92 | 0.468 | 12.38 | 0.174 | 20.40 | 0.153 | 21.45 | 0.159 | 21.46 | 0.120 | 23.41 | 0.118 | 23.50 | |
Woman | 0.172 | 21.24 | 0.406 | 14.40 | 0.121 | 24.43 | 0.100 | 25.98 | 0.140 | 23.63 | 0.062 | 30.04 | 0.055 | 31.13 | |
avg | 0.207 | 18.95 | 0.386 | 14.07 | 0.148 | 22.03 | 0.112 | 24.19 | 0.135 | 23.01 | 0.091 | 26.10 | 0.089 | 26.40 | |
0.3 | Lena | 0.195 | 19.49 | 0.365 | 14.48 | 0.094 | 25.82 | 0.075 | 27.70 | 0.086 | 26.80 | 0.063 | 29.24 | 0.061 | 29.40 |
A.ort | 0.135 | 19.36 | 0.192 | 16.41 | 0.074 | 24.65 | 0.078 | 24.10 | 0.076 | 24.53 | 0.057 | 26.85 | 0.055 | 27.08 | |
B.oon | 0.223 | 18.60 | 0.340 | 15.27 | 0.160 | 21.54 | 0.150 | 21.95 | 0.158 | 21.96 | 0.128 | 23.33 | 0.128 | 23.28 | |
B.ara | 0.247 | 18.64 | 0.373 | 15.42 | 0.114 | 25.26 | 0.100 | 26.32 | 0.113 | 25.59 | 0.085 | 27.75 | 0.081 | 28.05 | |
House | 0.156 | 20.55 | 0.303 | 15.14 | 0.071 | 27.39 | 0.053 | 29.77 | 0.073 | 27.39 | 0.052 | 30.02 | 0.047 | 30.87 | |
P.ers | 0.282 | 16.52 | 0.467 | 12.73 | 0.135 | 22.84 | 0.084 | 26.75 | 0.100 | 25.57 | 0.071 | 28.25 | 0.069 | 28.49 | |
S.oat | 0.221 | 18.22 | 0.431 | 12.99 | 0.132 | 22.66 | 0.119 | 23.47 | 0.128 | 23.14 | 0.098 | 25.13 | 0.097 | 25.19 | |
Woman | 0.179 | 20.96 | 0.374 | 15.00 | 0.087 | 27.17 | 0.058 | 30.61 | 0.098 | 26.48 | 0.050 | 31.90 | 0.042 | 33.47 | |
avg | 0.205 | 19.04 | 0.356 | 14.68 | 0.108 | 24.67 | 0.090 | 26.33 | 0.104 | 25.18 | 0.075 | 27.81 | 0.073 | 28.23 |
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Wang, W.; Zheng, J.; Zhao, L.; Chen, H.; Zhang, X. A Non-Local Tensor Completion Algorithm Based on Weighted Tensor Nuclear Norm. Electronics 2022, 11, 3250. https://doi.org/10.3390/electronics11193250
Wang W, Zheng J, Zhao L, Chen H, Zhang X. A Non-Local Tensor Completion Algorithm Based on Weighted Tensor Nuclear Norm. Electronics. 2022; 11(19):3250. https://doi.org/10.3390/electronics11193250
Chicago/Turabian StyleWang, Wenzhe, Jingjing Zheng, Li Zhao, Huiling Chen, and Xiaoqin Zhang. 2022. "A Non-Local Tensor Completion Algorithm Based on Weighted Tensor Nuclear Norm" Electronics 11, no. 19: 3250. https://doi.org/10.3390/electronics11193250
APA StyleWang, W., Zheng, J., Zhao, L., Chen, H., & Zhang, X. (2022). A Non-Local Tensor Completion Algorithm Based on Weighted Tensor Nuclear Norm. Electronics, 11(19), 3250. https://doi.org/10.3390/electronics11193250