Jyothula Sunil Kumar ,N Durga Sowdamini ,




Tensor Completion,Tensor Singular Value Decomposition,Discrete Cosine Transform,Convex Optimization,


Tensor Completion from a limited number of non-distorted observations, has enticed researchers interest. The color image has been considered as the three dimensional tensor. Low rank property in Optimization has been used to recover the tensors in the image. The Low rank prior alone not enough to tensor completion. The traditional tensor truncated nuclear norm approaches have been able to approximate the real rank of the tensor, but these are low rank prior approaches. Here a transformation-based optimization method has been proposed to complete the tensors of the image. The Discrete Cosine Transformation (DCT) has been used as transformation method. The tensor singular value decomposition (t-SVD) and accelerated proximal gradient line (APGL) approaches have been considered. The Full Reference metrics i.e., peak signal to noise ratio (PSNR) and structural similarity (SSIM) have been used to evaluate the proposed approach. The obtained results are superior to the existing algorithms. The PSNR and SSIM have been recorded as 27.30 dB and 0.8845 respectively


I. Emmanuel J Candès and Benjamin Recht. Exact matrix completion via convex optimization. Foundations of Computational mathematics, 9(6):717, 2009.

II. Ji Liu, Przemyslaw Musialski, Peter Wonka, and Jieping Ye. Tensor completion for estimating missing values in visual data. IEEE transactions on pattern analysis and machine intelligence, 35(1):208–220, 2012.

III. Jing Dong, Zhichao Xue, Jian Guan, Zi-Fa Han, and Wenwu Wang. Low rank matrix completion using truncated nuclear norm and sparse regularizer. Signal Processing: Image Communication, 68:76–87, 2018.

IV. Misha E Kilmer, Karen Braman, Ning Hao, and Randy C Hoover. Third-order tensors as operators on matrices: A theoretical and computational framework with applications in imaging. SIAM Journal on Matrix Analysis and Applications, 34(1):148–172, 2013.

V. Ping-Ping Wang, Liang Li, and Guang-Hui Cheng. Low rank tensor completion with sparse regularization in a transformed domain. arXiv preprint arXiv:1911.08082, 2019.

VI. Shengke Xue, Wenyuan Qiu, Fan Liu, and Xinyu Jin. Low-rank tensor completion by truncated nuclear norm regularization. In 2018 24th International Conference on Pattern Recognition (ICPR), pages 2600–2605. IEEE, 2018.

VII. Yao Hu, Debing Zhang, Jieping Ye, Xuelong Li, and Xiaofei He. Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE transactions on pattern analysis and machine intelligence, 35(9):2117–2130, 2012.

VIII. Yaru Su, Xiaohui Wu, and Wenxi Liu. Low-rank tensor completion by sum of tensor nuclear norm minimization. IEEE Access, 7:134943–134953, 2019.

IX. Yunhe Wang, Chang Xu, Shan You, Chao Xu, and Dacheng Tao. Dct regularized extreme visual recovery. IEEE Transactions on Image Processing, 26(7):3360–3371, 2017.

X. Zemin Zhang, Gregory Ely, Shuchin Aeron, Ning Hao, and Misha Kilmer. Novel methods for multilinear data completion and de-noising based on tensor-svd. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3842–3849, 2014.

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