Low Tensor Rank Constrained Image Inpainting Using a Novel Arrangement Scheme
Source abstract
Abstract
Employing low tensor rank decomposition in image inpainting has attracted increasing attention. This study exploited novel tensor arrangement schemes to transform an image (a low-order tensor) to a higher-order tensor without changing the total number of pixels. The developed arrangement schemes enhanced the low rankness of images under three tensor decomposition methods: matrix SVD, tensor train (TT) decomposition, and tensor singular value decomposition (t-SVD). By exploiting the schemes, we solved the image inpainting problem with three low-rank constrained models that use the matrix rank, TT rank, and tubal rank as constrained priors. The tensor tubal rank and tensor train multi-rank were developed from t-SVD and TT decomposition, respectively. Then, ADMM algorithms were efficiently exploited for solving the three models. Experimental results demonstrate that our methods are effective for image inpainting and superior to numerous close methods.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Advanced Image Processing Techniques · Image and Signal Denoising Methods · Generative Adversarial Networks and Image Synthesis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Space Information, Space Engineering University, Beijing 101400, China
China Academy of Space Technology (Xi’an), Xi’an 710100, China
Funding
National Key Laboratory of Science and Technology on Space Microwave · Science and Technology Innovation Cultivation Fund of Space Engineering University · Information Security Laboratory of National Defense Research and Experiment
References (50)
Show source-provided references
1. Light field inpainting propagation via low rank matrix completion10.1109/TIP.2018.2791864 ↗
2. A new nonconvex approach to low-rank matrix completion with application to image inpainting, Multidim
3. A low-rank tensor dictionary learning method for hyperspectral image denoising10.1109/TSP.2020.2971441 ↗
4. Low-Rank tensor completion based on nonconvex regularization10.1016/j.sigpro.2023.109157 ↗
5. Recovering low-rank tensor from limited coefficients in any ortho-normal basis using tensor-singular value decomposition10.1049/sil2.12017 ↗
6. Image completion using low tensor tree rank and total variation minimization10.1109/TMM.2018.2859026 ↗
7. Accurate regularized Tucker decomposition for image restoration10.1016/j.apm.2023.06.031 ↗
8. Low rank tensor completion for multiway visual data10.1016/j.sigpro.2018.09.039 ↗
9. Tensor decompositions and applications10.1137/07070111X ↗
10. Third-order tensors as operators on matrices: A theoretical and computational framework with applications in imaging10.1137/110837711 ↗
11. Tensor-based formulation and nuclear norm regularization for multienergy computed tomography10.1109/TIP.2014.2305840 ↗
12. Tensor factorization for low-rank tensor completion10.1109/TIP.2017.2762595 ↗
13. TT-cross approximation for multidimensional arrays10.1016/j.laa.2009.07.024 ↗
14. Tensor-train decomposition10.1137/090752286 ↗
15. A new scheme for the tensor representation10.1007/s00041-009-9094-9 ↗
16. Zhao, Q., Zhou, G., Xie, S., Zhang, L., and Cichocki, A. (2016). Tensor ring decomposition. arXiv.
17. Fully-connected tensor network decomposition and its application to higher-order tensor completion
18. Exact tensor completion using T-SVD10.1109/TSP.2016.2639466 ↗
19. Tensor robust principal component analysis with a new tensor nuclear norm10.1109/TPAMI.2019.2891760 ↗
20. Unifying tensor factorization and tensor nuclear norm approaches for low-rank tensor completion10.1016/j.neucom.2021.06.020 ↗
21. Simultaneous tensor decomposition and completion using factor priors10.1109/TPAMI.2013.164 ↗
22. Enhanced sparsity prior model for low-rank tensor completion10.1109/TNNLS.2019.2956153 ↗
23. Tensor completion for estimating missing values in visual data10.1109/TPAMI.2012.39 ↗
24. Low-Rank Tensor Completion and Total Variation Minimization for Color Image Inpainting10.1109/ACCESS.2020.2980058 ↗
25. Smooth PARAFAC decomposition for tensor completion10.1109/TSP.2016.2586759 ↗
26. Yokota, T., and Hontani, H. (2017, January 21–26). Simultaneous visual data completion and denoising based on tensor rank and total variation minimization and its primal-dual splitting algorithm. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, USA.10.1109/CVPR.2017.409 ↗
27. Li, L., Jiang, F., and Shen, R. (2018, January 7–10). Total Variation Regularized Reweighted Low-rank Tensor Completion for Color Image Inpainting. Proceedings of the 25th IEEE International Conference on Image Processing (ICIP), Athens, Greece.10.1109/ICIP.2018.8451530 ↗
28. Bayesian CP factorization of incomplete tensors with automatic rank determination10.1109/TPAMI.2015.2392756 ↗
29. Bayesian robust tensor completion via CP decomposition10.1016/j.patrec.2022.10.005 ↗
30. A Bayesian robust CP decomposition approach for missing traffic data imputation10.1007/s11042-022-13069-7 ↗
31. Multidimensional clinical data denoising via Bayesian CP factorization10.1007/s11431-018-9493-9 ↗
32. Fully-connected tensor network decomposition for robust tensor completion problem10.3934/ipi.2023030 ↗
33. Robust tensor completion via capped Frobenius norm10.1109/TNNLS.2023.3236415 ↗
34. Efficient tensor completion for color image and video recovery: Low-Rank Tensor Train10.1109/TIP.2017.2672439 ↗
35. Ma, S., Du, H., Hu, J., Wen, X., and Mei, W. (2019, January 19–21). Image inpainting exploiting tensor train and total variation. Proceedings of the 12th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), Suzhou, China.10.1109/CISP-BMEI48845.2019.8965787 ↗
36. Ma, S. (2021, January 22–24). Video inpainting exploiting tensor train and sparsity in frequency domain. Proceedings of the IEEE 6th International Conference on Signal and Image Processing (ICSIP), Nanjing, China.10.1109/ICSIP52628.2021.9688906 ↗
37. Dynamic MR image reconstruction from highly undersampled (k, t)-space data exploiting low tensor train rank and sparse prior10.1109/ACCESS.2020.2972316 ↗
38. Latorre, J. (2018, March 03). Image Compression and Entanglement. Available online: https://arxiv.org/abs/quant-ph/0510031.
39. Factorization strategies for third-order tensors10.1016/j.laa.2010.09.020 ↗
40. An order-p tensor factorization with applications in imaging10.1137/110841229 ↗
41. Oseledets, I. (2009, January 19–21). Compact matrix form of the d-dimensional tensor decomposition. Proceedings of the International Symposium on Nonlinear Theory and Its Applications, Sapporo, Japan.
42. Accelerated dynamic MRI exploiting sparsity and low-rank structure: K-t SLR10.1109/TMI.2010.2100850 ↗
43. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization10.1137/070697835 ↗
44. Signoretto, M., Cevher, V., and Suykens, J. (2013, January 10–13). An SVD-free approach to a class of structured low rank matrix optimization problems with application to system identification. Proceedings of the IEEE Conference on Decision and Control (CDC), Firenze, Italy. no. EPFL-CONF-184990.
45. Nonlocal gradient sparsity regularization for image restoration10.1109/TCSVT.2016.2556498 ↗
46. Hyperspectral Unmixing Using Sparsity-Constrained Deep Nonnegative Matrix Factorization with Total Variation10.1109/TGRS.2018.2834567 ↗
47. Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm10.1007/s12532-012-0044-1 ↗
48. Ai, J., Ma, S., Du, H., and Fang, L. (2018, January 12–16). Dynamic MRI Reconstruction Using Tensor-SVD. Proceedings of the 14th IEEE International Conference on Signal Processing, Beijing, China.10.1109/ICSP.2018.8652421 ↗
49. Image quality assessment: From error visibility to structural similarity10.1109/TIP.2003.819861 ↗
50. Fast and Accurate Tensor Completion with Total Variation Regularized Tensor Trains10.1109/TIP.2020.2995061 ↗