Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion

Jing LIU; Han LIU; Kaiyu HUANG; Liyu SU

doi:10.11999/JEIT181076

Volume 41 Issue 11

Nov. 2019

Turn off MathJax

Article Contents

Article Navigation > Journal of Electronics & Information Technology > 2019 > 41(11): 2787-2794

Jing LIU, Han LIU, Kaiyu HUANG, Liyu SU. Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion[J]. Journal of Electronics & Information Technology, 2019, 41(11): 2787-2794. doi: 10.11999/JEIT181076

Citation:

Jing LIU, Han LIU, Kaiyu HUANG, Liyu SU. Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion[J]. Journal of Electronics & Information Technology, 2019, 41(11): 2787-2794. doi: 10.11999/JEIT181076

Citation:

PDF( 1922 KB)

Automatic Rank Estimation Based Riemannian Optimization Matrix Completion Algorithm and Application to Image Completion

doi: 10.11999/JEIT181076

1.
School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
2.
Ministry of Education Key Laboratory for Intelligent Networks and Network Security, Xi’an Jiaotong University, Xi’an 710049, China

Funds: The National Natural Science Foundation of China (61573276)

Received Date: 2018-11-23
Rev Recd Date: 2019-05-07

Available Online: 2019-05-20

Publish Date: 2019-11-01

Abstract

Abstract

As an extension of Compressed Sensing(CS), Matrix Completion(MC) is widely applied to different fields. Recently, the Riemannian optimization based MC algorithm attracts a lot of attention from researchers due to its high accuracy in reconstruction and computational efficiency. Considering that the Riemannian optimization based MC algorithm assumes a fixed rank of the original matrix, and selects a random initial point for iteration, a novel algorithm is proposed, namely automatic rank estimation based Riemannian optimization matrix completion algorithm. In the proposed algorithm, the estimate of rank is obtained minimizing the objective function that involving the rank regulation, in addition, the iterative starting point is optimized based on Riemannian manifold. The Riemannian manifold based conjugate gradient method is then used to complete the matrix, thereby improving the reconstruction precision. The experimental results demonstrate that the image completion performance is significantly improved using the proposed algorithm, compared with several classical image completion methods.
- Image Completion(IC),
- Matrix Completion(MC),
- Automatic rank estimation,
- Riemannian optimization,
- Convolutional Neural Network (CNN)

FullText(HTML)

References(18)

References

臧芳. 一种利用低秩矩阵填充技术恢复气象数据的方法[J]. 计算机应用与软件, 2017, 34(9): 322–327. doi: 10.3969/j.issn.1000-386x.2017.09.063

ZANG Fang. Method of restoring meteorological data using low-rank matrix filling technique[J]. Computer Applications and Software, 2017, 34(9): 322–327. doi: 10.3969/j.issn.1000-386x.2017.09.063

杨国亮, 鲁海荣, 丰义琴, 等. 基于非局部矩阵填充的文物修复技术研究[J]. 计算机应用与软件, 2016, 33(11): 126–129. doi: 10.3969/j.issn.1000-386x.2016.11.030

YANG Guoliang, LU Hairong, FENG Yiqin, et al. On cultural relic images restoration technology based on non-local matrix completion[J]. Computer Applications and Software, 2016, 33(11): 126–129. doi: 10.3969/j.issn.1000-386x.2016.11.030

陈秋实, 杨强, 董英凝, 等. 基于矩阵填充的合成宽带高频雷达非网格目标分辨技术研究[J]. 电子与信息学报, 2017, 39(12): 2874–2880. doi: 10.11999/JEIT170449

CHEN Qiushi, YANG Qiang, DONG Yingning, et al. Off-the-grid targets resolution of synthetic bandwidth high frequency radar based on matrix completion[J]. Journal of Electronics &Information Technology, 2017, 39(12): 2874–2880. doi: 10.11999/JEIT170449

CAI T T and ZHANG Anru. Sparse representation of a polytope and recovery of sparse signals and low-rank matrices[J]. IEEE Transactions on Information Theory, 2014, 60(1): 122–132. doi: 10.1109/TIT.2013.2288639

CAI Jianfeng, CANDES E J, and SHEN Zuowei. A singular value thresholding algorithm for matrix completion[J]. SIAM Journal on Optimization, 2010, 20(4): 1956–1982. doi: 10.1137/080738970

LIN Zhouchen, CHEN Minming, and MA Yi. The augmented lagrange multiplier method for exact recovery of corrupted low-rank matrices[J]. arXiv preprint arXiv: 1009.5055, 2010.

VANDEREYCKEN B. Low-rank matrix completion by riemannian optimization[J]. SIAM Journal on Optimization, 2013, 23(2): 1214–1236. doi: 10.1137/110845768

MEKA R, JAIN P, and DHILLON I S. Guaranteed rank minimization via singular value projection[C]. Proceedings of the Neural Information Processing Systems Conference, Vancouver, Canada, 2010: 937–945.

KESHAVAN R H and OH S. A gradient descent algorithm on the grassman manifold for matrix completion[J]. arXiv preprint arXiv: 0910.5260, 2009.

SHI Qiquan, LU Haiping, and CHEUNG Y. Rank-one matrix completion with automatic rank estimation via L1-norm regularization[J]. IEEE Transactions on Neural Networks and Learning Systems, 2018, 29(10): 4744–4757. doi: 10.1109/TNNLS.2017.2766160

陈蕾, 陈松灿. 矩阵补全模型及其算法研究综述[J]. 软件学报, 2017, 28(6): 1547–1564. doi: 10.13328/j.cnki.jos.005260

CHEN Lei and CHEN Songcan. Survey on matrix completion models and algorithms[J]. Journal of Software, 2017, 28(6): 1547–1564. doi: 10.13328/j.cnki.jos.005260

CANDÈS E J and RECHT B. Exact matrix completion via convex optimization[J]. Foundations of Computational Mathematics, 2009, 9(6): 717–772. doi: 10.1007/s10208-009-9045-5

LI Wei, ZHAO Lei, LIN Zhijie, et al. Non-local image inpainting using low‐rank matrix completion[J]. Computer Graphics Forum, 2015, 34(6): 111–122. doi: 10.1111/cgf.12521

LIU Ping, LEWIS J, and RHEE T. Low-rank matrix completion to reconstruct incomplete rendering images[J]. IEEE Transactions on Visualization and Computer Graphics, 2018, 24(8): 2353–2365. doi: 10.1109/TVCG.2017.2722414

DONG Bin, MAO Yu, OSHER S, et al. Fast linearized Bregman iteration for compressive sensing and sparse denoising[J]. Communications in Mathematical Sciences, 2010, 8(1): 93–111. doi: 10.4310/CMS.2010.v8.n1.a6

LIU Yuanyuan, SHANG Fanhua, WEI Fan, et al. Generalized higher-order orthogonal iteration for tensor decomposition and completion[C]. Proceedings of the 27th International Conference on Neural Information Processing Systems, Montreal, Canada, 2014: 1763–1771.

HORE A and ZIOU D. Image quality metrics: PSNR vs. SSIM[C]. Proceedings of the 20th International Conference on Pattern Recognition, Istanbul, Turkey, 2010: 2366–2369.

ÖZIÇ M Ü and ÖZŞEN S. A new model to determine asymmetry coefficients on MR images using PSNR and SSIM[C]. Proceedings of 2017 International Artificial Intelligence and Data Processing Symposium, Malatya, Turkey, 2017: 1–6.

Relative Articles

Supplements(0)

Cited By

Proportional views