Abstract
In the traditional non-local similar patches based denoising algorithms, the image patches are firstly flatted into a vector, which ignores the spatial layout information within the image patches that can be used for improving the denoising performance. To deal with this issue, we propose a weighted tensor Schatten p-norm minimization (WTSN) algorithm for image denoising and use alternating direction method (ADM) to solve it. In WTSN, the image patches are treated as matrix instead of vectorizing them, and thus make full use of information within the structure of the image patches. Furthermore, the employed Schatten p-norm requires much weaker incoherence conditions and can find sparser solutions than the nuclear norm, and thus is more robust against noise and outliers. Experimental results show that the proposed WTSN algorithm outperforms many state-of-the-art denoising algorithms in terms of both quantitative measure and visual perception quality.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
J. Portilla, V. Strela, M.J. Wainwright, E.P. Simoncelli, Image denoising using scale mixtures of gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)
A.L.D. Cunha, J. Zhou, M.N. Do, The nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans. Image Process. 15(10), 3089–3101 (2006)
W. Dong, G. Shi, X. Li, Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans. Image Process. 22(2), 700–11 (2013)
S. Gu, L. Zhang, W. Zuo, and X. Feng. Weighted nuclear norm minimization with application to image denoising, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2014)
A. Buades, B. Coll, J.M. Morel, A non-local algorithm for image denoising, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005)
A. Eriksson, A.V.D. Hengel, Efficient computation of robust low-rank matrix approximations in the presence of missing data using the l1 norm, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2010)
A.M. Buchanan, A.W. Fitzgibbon, Damped Newton algorithms for matrix factorization with missing data, in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (2005)
M. Partridge, M. Jabri, Robust principal component analysis, in Proceedings of IEEE Signal Processing Society Workshop (2000)
M. Fazel, H. Hindi, S.P. Boyd, A rank minimization heuristic with application to minimum order system approximation, in Proceedings of American Control Conference (2001)
E.J. Candes, B. Recht, Exact low-rank matrix completion via convex optimization, in Proceedings of Allerton Conference on Communication, Control, and Computing (2008)
J.F. Cai, E.J. Cands, Z. Shen, A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2008)
R. Chartrand, Exact reconstruction of sparse signals via nonconvex minimization. IEEE Signal Process. Lett. 14(10), 707–710 (2007)
F. Nie, H. Huang, C. Ding, Low-rank matrix recovery via efficient Schatten p-norm minimization, in Proceedings of AAAI Conference on Artificial Intelligence (2012)
K. Mohan, M. Fazel, Iterative reweighted algorithms for matrix rank minimization. J. Mach. Learn. Res. 13(1), 3441–3473 (2012)
L. Liu, W. Huang, D. Chen, Exact minimum rank approximation via schatten p-norm minimization. J. Comput. Appl. Math. 267(6), 218–227 (2014)
X. Zhang, D. Wang, Z. Zhou, Y. Ma, Simultaneous rectification and alignment via robust recovery of low-rank tensors, in Proceedings of Advances in Neural Information Processing Systems (2013)
X. Zhang, Z. Zhou, D. Wang, Y. Ma, Hybrid singular value thresholding for tensor completion, in Proceedings of AAAI Conference on Artificial Intelligence (2014)
W. Zuo, D. Meng, L. Zhang, X. Feng, A generalized iterated shrinkage algorithm for non-convex sparse coding, in Proceedings of IEEE International Conference on Computer Vision (2013)
K. Dabov, A. Foi, V. Katkovnik, K. Egiazarian, Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)
Y. Xie, S. Gu, Y. Liu, W. Zuo, W. Zhang, L. Zhang, Weighted schatten p-norm minimization for image denoising and background subtraction. IEEE Trans. Image Process. 25(10), 4842–4857 (2015)
P. Chatterjee, P. Milanfar, Patch-based near-optimal image denoising. IEEE Trans. Image Process. 21(4), 1635–1649 (2012)
D. Zoran, Y. Weiss, From learning models of natural image patches to whole image restoration, in Proceedings of IEEE International Conference on Computer Vision (2011)
H. Talebi, P. Milanfar, Global image denoising. IEEE Trans. Image Process. 23(2), 755–768 (2014)
Acknowledgements
This work is supported in part by the National Natural Science Foundation of China [grant nos. 61772374, 61503263, 61472285], in part by the Zhejiang Provincial Natural Science Foundation [grant nos. LY17F030004, LR17F030001, LY16F020023], in part by the project of science and technology plans of Zhejiang Province (Grants no. 2015C31168), in part by the Key Innovative Team Support and Project of science and technology plans of Wenzhou City [grant nos. C20170008, G20160002, G20150017, ZG2017016].
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Yan, Y., Zhang, X., Zheng, J., Zhao, L. (2019). Weighted Tensor Schatten p-norm Minimization for Image Denoising. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2018 Chinese Intelligent Systems Conference. Lecture Notes in Electrical Engineering, vol 528. Springer, Singapore. https://doi.org/10.1007/978-981-13-2288-4_17
Download citation
DOI: https://doi.org/10.1007/978-981-13-2288-4_17
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-2287-7
Online ISBN: 978-981-13-2288-4
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)