Low-rank approximation-based methods have recently achieved impressive results in image restoration. Generally, the low-rank constraint integrated with the nonlocal self-similarity prior is enforced for image recovery. However, it is still unsatisfactory to recover complex image structures due to the lack of joint modeling based on local and global information, especially when the signal-to-noise ratio is low. In this paper, we propose a novel structure-constrained low-rank approximation method using complementary local and global information, as, respectively, modeled by kernel Wiener filtering and low-rank regularization. The proposed method solves the ill-posed inverse problem associated with image denoising by the alternating direction method of multipliers. Experimental results demonstrate that the proposed method not only removes noise effectively, but also is highly competitive against the state-of-the-art methods both qualitatively and quantitatively.
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Allan Weber, The USC-SIPI Image Database, March 31, 2013, http://sipi.usc.edu/database/.
Member of SoftWays’ Medical Imaging Group, Brain MRI Images, March 31, 2013, https://www.mr-tip.com/serv1.php?type=db.
Alexander Wong, David A. Clausi, Paul Fieguth, Skin Cancer Detection, March 31, 2018, https://uwaterloo.ca/vision-image-processing-lab/research-demos/skin-cancer-detection.
Jun Xu, Hui Li, Zhetong Liang, David Zhang, Lei Zhang, PolyU Real-World Images Dataset, March 31, 2019, https://github.com/csjunxu/PolyU-Real-World-Noisy-Images-Dataset.
Thomas L. Diepgen, Dermatology Information System, March 31, 2013, http://www.dermis.net.
Baselice F, Ferraioli G, Pascazio V, Sorriso A (2019) Denoising of MR images using Kolmogorov–Smirnov distance in a non local framework. Magn Reonance Imaging 57:176–193
Ben Abdallah M, Malek J, Azar AT, Belmabrouk H, Monreal JE, Krissian K (2016) Adaptive noise-reducing anisotropic diffusion filter. Neural Comput Appl 27(5):1273–1300
Benou A, Veksler R, Friedman A, Raviv TR (2017) Ensemble of expert deep neural networks for spatio-temporal denoising of contrast-enhanced MRI sequences. Med Image Anal 42:145–159
Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122
Buades A, Coll B, Morel JM (2005) A review of image denoising algorithms, with a new one. Multiscale Model Simul 4(2):490–530
Cai JF, Candes EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982
Candes EJ, Recht B (2009) Exact matrix completion via convex optimization. Found Comput Math 9(6):717–772
Candes EJ, Li XD, Ma Y, Wright J (2011) Robust principal component analysis? J ACM 58(3):11:1–11:37
Dabov K, Foi A, Katkovnik V, Egiazarian K (2007) Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095
Daubechies I, Defrise M, De Mol C (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun Pure Appl Math 57(11):1413–1457
Divakar N, Babu RV (2017) Image denoising via CNNs: an adversarial approach. In: 2017 IEEE conference on computer vision and pattern recognition workshops (CVPRW), Honolulu, HI, 21–26 July 2017, pp 1076–1083
Elad M, Aharon M (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans Image Process 15(12):3736–3745
Fan F, Ma Y, Li C, Mei X, Huang J, Ma J (2017) Hyperspectral image denoising with superpixel segmentation and low-rank representation. Inf Sci 397:48–68
Fan L, Li X, Guo Q, Zhang C (2018) Nonlocal image denoising using edge-based similarity metric and adaptive parameter selection. Sci China Inf Sci 61(4):049101
Gu SH, Xie Q, Meng DY, Zuo WM, Feng XC, Zhang L (2017) Weighted nuclear norm minimization and its applications to low level vision. Int J Comput Vis 121(2):183–208
Hu Y, Zhang DB, Ye JP, Li XL, He XF (2013) Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE Trans Pattern Anal Mach Intell 35(9):2117–2130
Huang YM, Yan HY, Wen YW, Yang X (2018) Rank minimization with applications to image noise removal. Inf Sci 429:147–163
Irshad M, Muhammad N, Sharif M, Yasmeen M (2018) Automatic segmentation of the left ventricle in a cardiac MR short axis image using blind morphological operation. Eur Phys J Plus 133(4):148
Khalid S, Muhammad N, Sharif M (2018) Automatic measurement of the traffic sign with digital segmentation and recognition. IET Intell Transp Syst 13(2):269–279
Khan H, Sharif M, Bibi N, Muhammad N (2019) A novel algorithm for the detection of cerebral aneurysm using sub-band morphological operation. Eur Phys J Plus 134(1):34
Khan MA, Akram T, Sharif M, Javed MY, Muhammad N, Yasmin M (2019) An implementation of optimized framework for action classification using multilayers neural network on selected fused features. Pattern Anal Appl 22(4):1377–1397
Khan NS, Muhammad N, Farwa S, Saba T, Khattak S, Mahmood Z (2019) Early CU depth decision and reference picture selection for low complexity MV-HEVC. Symmetry 11(4):454
Mahmood Z, Bibi N, Usman M, Khan U, Muhammad N (2019) Mobile cloud based-framework for sports applications. Multidimens Syst Signal Process 30(4):1991–2019
Mughal B, Muhammad N, Sharif M, Rehman A, Saba T (2018) Removal of pectoral muscle based on topographic map and shape-shifting silhouette. BMC Cancer 18(1):778
Muhammad N, Bibi N, Jahangir A, Mahmood Z (2018) Image denoising with norm weighted fusion estimators. Pattern Anal Appl 21(4):1013–1022
Muhammad N, Bibi N, Wahab A, Mahmood Z, Akram T, Naqvi SR, Oh HS, Kim DG (2018) Image de-noising with subband replacement and fusion process using bayes estimators. Comput Electr Eng 70:413–427
Li H, He X, Tao D, Tang Y, Wang R (2018) Joint medical image fusion, denoising and enhancement via discriminative low-rank sparse dictionaries learning. Pattern Recognit 79:130–146
Liu HF, Xiong RQ, Liu D, Ma SW, Wu F, Gao W (2018) Image denoising via low rank regularization exploiting intra and inter patch correlation. IEEE Trans Circuits Syst Video Technol 28(12):3321–3332
Mairal J, Sapiro G, Elad M (2008) Learning multiscale sparse representations for image and video restoration. Multiscale Model Simul 7(1):214–241
Meiniel W, Olivo-Marin JC, Angelini ED (2018) Denoising of microscopy images: a review of the state-of-the-art, and a new sparsity-based method. IEEE Trans Image Process 27(8):3842–3856
Osher S, Burger M, Goldfarb D, Xu JJ, Yin WT (2005) An iterative regularization method for total variation-based image restoration. Multiscale Model Simul 4(2):460–489
Ozmen G, Ozsen S (2018) A new denoising method for fMRI based on weighted three-dimensional wavelet transform. Neural Comput Appl 29(8):263–276
Papari G, Idowu N, Varslot T (2017) Fast bilateral filtering for denoising large 3D images. IEEE Trans Image Process 26(1):251–261
Portilla J, Strela V, Wainwright MJ, Simoncelli EP (2003) Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans Image Process 12(11):1338–1351
Ran MS, Hu JR, Chen Y, Chen H, Sun HQ, Zhou JL, Zhang Y (2019) Denoising of 3D magnetic resonance images using a residual encoderdecoder Wasserstein generative adversarial network. Med Image Anal 55:165–180
Spiegelberg J, Idrobo JC, Herklotz A, Ward TZ, Zhou W, Rusz J (2018) Local low rank denoising for enhanced atomic resolution imaging. Ultramicroscopy 187:34–42
Tomasi C, Manduchi R (1998) Bilateral filtering for gray and color images. In: Proceedings of IEEE international conference on computer vision, Santa Barbara, CA, 23–25 June 1998, pp 839–846
Torralba A, Oliva A (2003) Statistics of natural image categories. Netw Comput Neural Syst 14(3):391–412
Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612
Wu Y, Fang LY, Li ST (2019) Weighted tensor rank-1 decomposition for nonlocal image denoising. IEEE Trans Image Process 28(6):2719–2730
Xiao J, Tian H, Zhang Y, Zhou Y, Lei J (2018) Blind video denoising via texture-aware noise estimation. Comput Vis Image Underst 169:1–13
Xu J, Li H, Liang Z, Zhang D, Zhang L (2018) Real-world noisy image denoising: a new benchmark. arXiv preprint arXiv:1804.02603
Yan Q, Xu Y, Yang X, Nguyen T (2015) Single image superresolution based on gradient profile sharpness. IEEE Trans Image Process 24(10):3187–3202
Yang Q, Yan P, Zhang Y, Yu H, Shi Y, Mou X, Kalra MK, Zhang Y, Sun L, Wang G (2018) Low-dose CT image denoising using a generative adversarial network with wasserstein distance and perceptual loss. IEEE Trans Med Imaging 37(6):1348–1357
Zhang CY, Hu WR, Jin TY, Mei ZL (2018) Nonlocal image denoising via adaptive tensor nuclear norm minimization. Neural Comput Appl 29(1):3–19
Zhang HJ, Wang S, Zhao MB, Xu XF, Ye YM (2018) Locality reconstruction models for book representation. IEEE Trans Knowl Data Eng 30(10):1873–1886
Zhang K, Zuo W, Chen Y, Meng D, Zhang L (2017) Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans Image Process 26(7):3142–3155
Zhang K, Zuo W, Zhang L (2018) FFDNet: toward a fast and flexible solution for CNN-based image denoising. IEEE Trans Image Process 27(9):4608–4622
Zhang Y, Liu J, Li M, Guo Z (2014) Joint image denoising using adaptive principal component analysis and self-similarity. Inf Sci 259:128–141
Zhang Y, Shi F, Cheng J, Wang L, Yap PT, Shen D (2019) Longitudinally guided super-resolution of neonatal brain magnetic resonance images. IEEE Trans Cybern 49(2):662–674
Zhang Y, Liu J, Yang W, Guo Z (2015) Image super-resolution based on structure-modulated sparse representation. IEEE Trans Image Process 24(9):2797–2810
Zhong XW, Xu LL, Li YT, Liu ZY, Chen EH (2015) A nonconvex relaxation approach for rank minimization problems. In: Proceedings of AAAI conference on artificial intelligence, Austin, Texas, USA, 25–30 January 2015, pp 1980–1987
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The authors declare that they have no conflict of interest.
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This work was supported by Natural Science Basic Research Program of Shaanxi (Program No. 2019JM-103), Open Research Fund of CAS Key Laboratory of Spectral Imaging Technology (Grant No. LSIT201920W), Social Science Foundation of Shaanxi Province (Grant No. 2019H010), Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT13090), and NVIDIA Corporation with the donation of the Titan Xp GPU used for this research.
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Zhang, Y., Kang, R., Peng, X. et al. Image denoising via structure-constrained low-rank approximation. Neural Comput & Applic (2020). https://doi.org/10.1007/s00521-020-04717-w
- Image denoising
- Sparse representation
- Low-rank approximation
- Wiener filtering
- Deep learning