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基于低秩高阶张量逼近的图像视频恢复
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Abstract:
图像视频恢复是计算机视觉中一项基本但关键的任务，近年来得到了广泛的研究。然而，现有的方法存在着不可避免的缺点：有些需要预定义秩，有些则无法处理高阶数据。为了克服这些缺点，本文利用图像视频数据通常具有的低秩性，采用低秩高阶张量逼近方法实现在混合噪音的环境下的彩色视频恢复。首先，本文建立了一个高阶张量代数框架。基于该框架，通过设计近端算子，提出了一种新的低秩高阶张量逼近(LRHA)方法，旨在从被高度污染的阶张量数据中恢复出潜在的低秩部分，从而完成图像视频恢复任务。设计了相应的算法，并且针对多项图像视频恢复任务的实验结果表明，LRHA方法在处理相应问题方面具有优越性。
Image and video recovery is a basic but key task in computer vision and has been widely studied in recent years. However, existing methods have inevitable disadvantages: some require pre-defined rank, while others cannot handle high-order data. In order to overcome these shortcomings, this paper uses the low-rank high-order tensor approximation method to realize color video recovery in mixed noise environment. Firstly, a high-order tensor algebraic framework is established. Based on the framework, a new low-rank high-order tensor approximation (LRHA) method is proposed by designing a proximal operator to recover potential low-rank parts from highly contaminated tensor data, so as to complete the task of image and video restoration. And the corresponding algorithm was designed. Experimental results of image and video restoration tasks show that LRHA has advantages in dealing with corresponding problems.
| [1] | Dong, W., Li, X., Zhang, L. and Shi, G. (2011) Sparsity-Based Image Denoising via Dictionary Learning and Structural Clustering. Conference on Computer Vision and Pattern Recognition 2011, Colorado Springs, 20-25 June 2011, 457-464. https://doi.org/10.1109/CVPR.2011.5995478 |
| [2] | Liu, Y. and Wang, Z. (2015) Simultaneous Image Fusion and Denoising with Adaptive Sparse Representation. IET Image Processing, 9, 347-357. |
| [3] | Rajpoot, N. and Butt, I. (2012) A Multiresolution Framework for Local Similarity Based Image Denoising. Pattern Recognition, 45, 2938-2951. https://doi.org/10.1016/j.patcog.2012.01.023 |
| [4] | Goldfarb, D. and Qin, Z. (2014) Robust Low-Rank Tensor Recovery: Models and Algorithms. SIAM Journal on Matrix Analysis and Applications, 35, 225-253. https://doi.org/10.1137/130905010 |
| [5] | Wright, J., Ganesh, A., Rao, S., Peng, Y. and Ma, Y. (2009) Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization. Advances in Neural Information Processing Systems, 22, 2080-2088. |
| [6] | Candès, E.J., Li, X., Ma, Y. and Wright, J. (2011) Robust Principal Component Analysis? Journal of the ACM, 58, Article No. 11. https://doi.org/10.1145/1970392.1970395 |
| [7] | Kiers, H.A.L. (2000) Towards a Standardized Notation and Terminology in Multiway Analysis. Journal of Chemometrics, 14, 105-122. |
| [8] | Liu, J., Musialski, P., Wonka, P. and Ye, J. (2013) Tensor Completion for Estimating Missing Values in Visual Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, 35, 208-220.
https://doi.org/10.1109/TPAMI.2012.39 |
| [9] | Liu, X., Jing, X.-Y., Tang, G., Wu, F. and Dong, X. (2020) Low-Rank Tensor Completion for Visual Data Recovery via the Tensor Train Rank-1 Decomposition. IET Image Processing, 14, 114-124. |
| [10] | Liu, Y. and Long, Z. (2019) Image Completion Using Low Tensor Tree Rank and Total Variation Minimization. IEEE Transactions on Multimedia, 21, 338-350. https://doi.org/10.1109/TMM.2018.2859026 |
| [11] | Oseledets, I.V. (2011) Tensor-Train Decomposition. SIAM Journal on Scientific Computing, 33, 2295-2317.
https://doi.org/10.1137/090752286 |
| [12] | Semerci, O., Hao, N., Kilmer, M.E. and Miller, E.L. (2014) Tensor-Based Formulation and Nuclear Norm Regularization for Multienergy Computed Tomography. IEEE Transactions on Image Processing, 23, 1678-1693.
https://doi.org/10.1109/TIP.2014.2305840 |
| [13] | Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z. and Yan, S. (2020) Tensor Robust Principal Component Analysis with a New Tensor Nuclear Norm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 42, 925-938.
https://doi.org/10.1109/TPAMI.2019.2891760 |
| [14] | Feng, J., Yang, L.T., Dai, G., Wang, W. and Zou, D. (2019) A Secure High-Order Lanczos-Based Orthogonal Tensor SVD for Big Data Reduction in Cloud Environment. IEEE Transactions on Big Data, 5, 355-367.
https://doi.org/10.1109/TBDATA.2018.2803841 |
| [15] | Song, G., Ng, M.K., and Zhang, X. (2019) Robust Tensor Completion Using Transformed Tensor SVD. arXiv preprint arXiv:1907.01113. |
| [16] | Zhang, X. (2019) A Nonconvex Relaxation Approach to Low-Rank Tensor Completion. IEEE Transactions on Neural Networks and Learning Systems, 30, 1659-1671. https://doi.org/10.1109/TNNLS.2018.2872583 |
| [17] | Martin, C.D., Shafer, R. and LaRue, B. (2013) An Order-P Tensor Factorization with Applications in Imaging. SIAM Journal on Scientific Computing, 35, A474-A490. https://doi.org/10.1137/110841229 |
| [18] | Tibshirani, R. (1996) Regression Shrinkage and Selection via the Lasso. Journal of the Royal Statistical Society: Series B (Methodological), 58, 267-288. https://doi.org/10.1111/j.2517-6161.1996.tb02080.x |
| [19] | Xu, Y., Hao, R., Yin, W. and Su, Z. (2017) Parallel Matrix Factorization for Low-Rank Tensor Completion. Inverse Problems and Imaging, 9, 601-624. https://doi.org/10.3934/ipi.2015.9.601 |
| [20] | Zhang, Z. and Aeron, S. (2016) Exact Tensor Completion Using T-SVD. IEEE Transactions on Signal Processing, 65, 1511-1526. https://doi.org/10.1109/TSP.2016.2639466 |
| [21] | Huang, B., Mu, C., Goldfarb, D. and Wright, J. (2015) Provable Models for Robust Low-Rank Tensor Completion. Pacific Journal of Optimization, 11, 339-364. |
