Abstract
In the past decade, the sparsity prior of image is investigated and utilized widely as the development of compressed sensing theory. The dictionary learning combined with the convex optimization methods promotes the sparse representation to be one of the state-of-the-art techniques in image processing, such as denoising, super-resolution, deblurring, and inpainting. Empirically, the sparser of image representation, the better of image restoration. In this work, the non-local clustering sparse representation is applied with optimized matching strategies of self-similar patches, which break through the bottleneck of search window (localization) and improve the estimation effect of the sparse coefficient. The experimental results show that the proposed method provides an effective suppression on noise, preserves more details of image and presents more comfortable visual experience.
Similar content being viewed by others
References
Buades, A., Coll, B., Morel, J.M.: A review of image de-noising algorithms with a new one. J. Multiscale Model. Simul. 4(5), 490–530 (2010)
Zhang, L., Dong, W., Zhang, D., Shi, G.: Two-stage image denoising by principal component analysis with local pixel grouping. Pattern Recogn. 43(4), 1531–1549 (2010)
Dabov, K., Foi, A., Katkovnik, V., et al.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)
Xu, J., Zhang, L., Zuo, W., Zhang, D., Feng, X.: Patch group based nonlocal self-similarity prior learning for image denoising, Proc. IEEE International Conference on Computer Vision, October (2015) pp. 64–78
Mairal, J., Bach, F., Ponce, J., Sapiro, G, Zisserman, A: Non-local sparse models for image restoration. Proc. IEEE International Conference on Computer Vision, September 2009, pp. 2272–2279
Dong, W., Shi, G., Li, X.: Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans. Image Process. 22(2), 700–711 (2012)
Huang, W., Wang, Q., Li, X.L.: Denoising-based multiscale feature fusion for remote sensing image captioning. IEEE Geosci. Remote Sens. Lett. 18(3), 436–440 (2021)
Yuan, Y., Lin, J.Z., Wang, Q.: Hyperspectral image classification via multitask joint sparse representation and stepwise MRF optimization. IEEE Transactions Cybern. 46(12), 2966–2977 (2016)
Kaur, M., Sharma, K., et al.: Image denoising using wavelet thresholding. Proc. Int. J. Eng. Comput. Sci. 2(10), 2932–2935 (2012)
Elad, M., et al.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3735–3746 (2006)
Zoran, D., Weiss, Y.: From learning models of natural image patches to whole image restoration, Proc. IEEE International Conference on Computer Vision, November (2011) pp. 479–486
Dong, W., Zhang, L., Shi, G., Li, X.: Nonlocally centralized sparse representation for image restoration. IEEE Image Processing Transactions 22(4), 1620–1630 (2012)
Wang, S., Zhang, L., Liang, Y.: Nonlocal spectral prior model for low-level vision, Proc. 11th Asian conference on Computer Vision, November (2012)
Candes, E.J., Recht, B.: Exact matrix completion via convex optimization. Found. Comput. Math. 9, 717–772 (2009)
Chen, F., Zhang, L., Yu, H. M.: External Patch Prior Guided Internal Clustering for Image Denoising, Proc. IEEE International Conference on Computer Vision, December (2015) pp 603–611
Guo, Q., Zhang, C.M., et al.: An efficient SVD-based method for image denoising. IEEE Trans. Circuits Syst. Video Technol. 26(5), 868–880 (2016)
Gu, S. H., Zhang, L. et al.: Weighted nuclear norm minimization with application to image denoising, Proc. IEEE Conference on Computer Vision and Pattern Recognition, June 2014, pp. 1–8
Xie, Y., Gu, S.H., et al.: Weighted schatten p-norm minimization for image denoising and background subtraction. IEEE Trans. Image Process. 25(10), 4842–4857 (2016)
Wu, T., Zhang, R., Jiao, Z. H. et al.: Adaptive spectral rotation via joint cluster and pairwise structure. IEEE Transactions on Knowledge and Data Engineering (Early Access), April (2021)
Zhang, R., Li, X. L., Zhang, H. Y. et al., “Geodesic Multi-Class SVM with Stiefel Manifold Embedding”, IEEE Transactions on Pattern Analysis and Machine Intelligence ( Early Access), March (2021)
Zhang, R., Li, X.L.: Unsupervised feature selection via data reconstruction and side information. IEEE Trans. Image Process. 29, 8097–8106 (2020)
Zhang, R., Zhang, H.Y., Li, X.L.: Robust multi-task learning with flexible manifold constraint. IEEE Trans. Pattern Anal. Mach. Intell. 43(6), 2150–2157 (2021)
Zhang, R., Tong, H. H.: Robust Principal Component Analysis with Adaptive Neighbors, 33rd Conference on Neural Information Processing Systems, (2019)
Gu, S.H., Xie, Q., et al.: Weighted nuclear norm minimization and its applications to low level vision. Int. J. Comput. Vision 121(7), 183–208 (2017)
Dong, W., Zhang, L. et al.: Centralized sparse representation for image restoration, Proc. IEEE International Conference on Computer Vision, November 2011, pp 1259–1266
Candes, E. J.: Compressive Sampling, Proceedings of the International Congress of Mathematicians, Madrid, Spain, (2006)
Candes, E.J., Romberg, J., Tao, T.: Robust uncertainty principles exact signal reconstruction from highly incomplete frequency information. IEEE Transactions Information Theory 52(2), 489–509 (2016)
Candes, E.J., Romberg, J.: Sparsity and incoherence in compressive sampling. Inverse Prolems 23, 969–985 (2017)
Daubechies, I., Defrise, M., Dye Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413–1457 (2004)
Zhang, L., Zuo, W.M.: Image restoration: from sparse and low-rank priors to deep priors. IEEE Signal Process. Mag. 34(5), 172–179 (2017)
Donoho, D.L.: De-noising by soft-thresholding. IEEE Trans. Inf. Theory 41(3), 613–627 (1995)
Sendur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)
Olshausen, B.A., Field, D.J.: Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381(13), 607–609 (1996)
Gordo, A., Almazan, J. et al.: Deep image retrieval: learning global representations for image search, Proc. European Conference on Computer Vision, September 2016, pp 241–257
Shlens, J: A Tutorial on Principal Component Analysis, arXiv:1404.1100, April (2014)
Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)
Zoran, D., Weiss, Y. et al.: Scale invariance and noise in natural images, Proc. IEEE 12th International Conference on Computer Vision, October 2009, pp 2209–2216
Chen, Y., Pock, T.: Trainable nonlinear reaction diffusion: a flexible framework for fast and effective image restoration. IEEE Transactions Pattern Anal. Mach. Intell. 39(6), 1256–1272 (2016)
Zhang, K., Zuo, W.M., et al.: Beyond a Gaussian Denoiser: residual learning of deep CNN for image denoising. IEEE Image Process. Transactions 26(7), 3142–3155 (2017)
Zhang, K., Zuo, W.M., Zhang, L.: Ffdnet: toward a fast and flexible solution for cnn based image denoising. IEEE Image Process. Transactions 27(9), 4608–4622 (2018)
Dong, W., Wang, P.Y., et al.: Denoising prior driven deep neural network for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 41(10), 2305–2318 (2019)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Zhou, T., Li, C., Zeng, X. et al. Sparse representation with enhanced nonlocal self-similarity for image denoising. Machine Vision and Applications 32, 110 (2021). https://doi.org/10.1007/s00138-021-01232-3
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00138-021-01232-3