Skip to main content
SpringerLink
Log in

Adaptive Graph Filtering with Intra-Patch Pixel Smoothing for Image Denoising

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

Graph filtering has recently attracted significant attention in signal processing. This study proposes an adaptive graph filtering method with intra-patch pixel smoothing (AWGF-PS) to improve the quality of denoised images. A detailed coefficient shrinkage algorithm is provided for the graph filter, which makes the noisy component in each graph frequency band adaptively shrink with its component significance. It replaces the traditional ideal low-pass graph filter and is better at removing image noise in the entire band. As for the design of the graph filters whose performance depends heavily on the topological structure among signals, we infer the graph from the super-pixels of similar patches by considering the smoothing attribute of intra-patch pixels. This graph fully exploits the relationship among the pixels in local areas. Moreover, it can achieve an efficient calculation of graph Fourier bases on a small-scale graph, which effectively enhances the graph filtering’s practicality. The experiments demonstrate that our AWGF-PS method suitably restores the denoised images. It outperforms several state-of-the-art model-based methods and is competitive with certain discriminative learning methods. In particular, it has more advantages in tackling images with significant noise.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability

The datasets analyzed in this study are available in the http://imageprocessing-place.com/root_files_V3/image_databases.htm.

References

  1. A. Asokan, J. Anitha, Adaptive cuckoo search based optimal bilateral filtering for denoising of satellite images. ISA Trans. 100, 308–321 (2020)

    Article  Google Scholar 

  2. A. Buades, B. Coll, J.M. Morel, A review of image denoising algorithms, with a new one. SIAM J. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Y. Chen, Y. Tang, N. Xu, L. Zhou, L. Zhao, Image denoising via adaptive eigenvectors of graph Laplacian. J. Electron. Imaging 25(4), 043019 (2016)

    Article  Google Scholar 

  4. 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)

    Article  MathSciNet  Google Scholar 

  5. S. Deng, J. Han, Efficient general sparse denoising with non-convex sparse constraint and total variation regularization. Digit. Signal Proc. 78, 259–264 (2018)

    Article  Google Scholar 

  6. W. Dong, P. Wang, W. Yin, G. Shi, F. Wu, X. Lu, Denoising prior driven deep neural network for image restoration. IEEE Trans. Pattern Anal. Mach. Intell. 41(10), 2305–2318 (2019)

    Article  Google Scholar 

  7. W. Dong, L. Zhang, G. Shi, X. Li, Nonlocally centralized sparse representation for image restoration. IEEE Trans. Image Process. 22(4), 1620–1630 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. M. Elad, M. Aharon, Image denoising via learned dictionaries and sparse representation. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (2006)

  9. H. Fan, J. Li, Q. Yuan, X. Liu, M. Ng, Hyperspectral image denoising with bilinear low rank matrix factorization. Sig. Process. 163, 132–152 (2019)

    Article  Google Scholar 

  10. Y. Fang, H. Zhang, Y. Ren, Graph regularised sparse NMF factorisation for imagery de-noising. IET Comput. Vis. 12(4), 466–475 (2018)

    Article  Google Scholar 

  11. M. Hein, J.Y. Audibert, U.V. Luxburg From graphs to manifolds - weak and strong pointwise consistency of graph Laplacians. In: Conference on Learning Theory (2005)

  12. E. Isufi, A. Loukas, A. Simonetto, G. Leus, Autoregressive moving average graph filtering. IEEE Trans. Signal Process. 65(2), 274–288 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Jia, S. Song, L. Yao, H. Li, Q. Zhang, Y. Bai, Z. Gui, Image denoising via sparse representation over grouped dictionaries with adaptive atom size. IEEE Access 5, 22514–22529 (2017)

    Article  Google Scholar 

  14. X. Jia, X. Feng, W. Wang Adaptive regularizer learning for low rank approximation with application to image denoising. In: IEEE International Conference on Image Processing (2016)

  15. X. Jia, X. Feng, W. Wang, Rank constrained nuclear norm minimization with application to image denoising. Sig. Process. 129, 1–11 (2016)

    Article  Google Scholar 

  16. Y. Jin, W. Jiang, J. Shao, J. Lu, An improved image denoising model based on nonlocal means filter. Math. Probl. Eng. 2018(PT.8), 8593934.1-8593934.12 (2018)

    MathSciNet  MATH  Google Scholar 

  17. Z. Kai, W. Zuo, Z. Lei, FFDNet: Toward a fast and flexible solution for CNN based image denoising. IEEE Trans. Image Process. 27(9), 4608–4622 (2018)

    Article  MathSciNet  Google Scholar 

  18. V. Kalofolias, How to learn a graph from smooth signals. Artif. Intell. Stat. 51, 920–929 (2016)

    Google Scholar 

  19. Y. Li, J. Zhang, M. Wang, Improved BM3D denoising method. IET Image Proc. 11(12), 1197–1204 (2017)

    Article  Google Scholar 

  20. X. Liu, Y. Chen, NLTV-Gabor-based models for image decomposition and denoising. SIViP 14(2), 305–313 (2020)

    Article  Google Scholar 

  21. X. Liu, D. Zhai, D. Zhao, G. Zhai, W. Gao, Progressive image denoising through hybrid graph Laplacian regularization: A unified framework. IEEE Trans. Image Process. 23(4), 1491–1503 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. G. Mateos, S. Segarra, A.G. Marques, A. Ribeiro, Connecting the dots: identifying network structure via graph signal processing. IEEE Signal Process. Mag. 36(3), 16–43 (2019)

    Article  Google Scholar 

  23. F.G. Meyer, X. Shen, Perturbation of the eigenvectors of the graph Laplacian: application to image denoising. Appl. Comput. Harmon. Anal. 36(2), 326–334 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  24. M. Onuki, S. Ono, M. Yamagishi, Y. Tanaka, Graph signal denoising via trilateral filter on graph spectral domain. IEEE Trans. Signal Inf. Process. Netw 2(2), 137–148 (2016)

    MathSciNet  Google Scholar 

  25. A. Ortega, P. Frossard, J. Kovačević, J.M.F. Moura, P. Vandergheynst, Graph signal processing: overview, challenges, and applications. Proc. IEEE 106(5), 808–828 (2018)

    Article  Google Scholar 

  26. J. Pang, G. Cheung, Graph Laplacian regularization for image denoising: analysis in the continuous domain. IEEE Trans. Image Process 26(4), 1770–1785 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  27. H. Peng, R. Rao, S.A. Dianat, Multispectral image denoising with optimized vector bilateral filter. IEEE Trans. Image Process. 23(1), 264–273 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  28. N. Perraudin, J. Paratte, D.I. Shuman, V. Kalofolias, P. Vandergheynst, D.K. Hammond, GSPBOX: A Toolbox for Signal Processing on Graphs (Computer Science, Mathematics ArXiv, 2014)

  29. L. Qiao, L. Zhang, S. Chen, D. Shen, Data-driven graph construction and graph learning: a review. Neurocomputing 312, 336–351 (2018)

    Article  Google Scholar 

  30. S. Routray, A. Ray, C. Mishra, An efficient image denoising method based on principal component analysis with learned patch groups. SIViP 13(7), 1405–1412 (2019)

    Article  Google Scholar 

  31. C. Shan, X. Guo, J. Ou, Residual learning of deep convolutional neural networks for image denoising. J. Intell. Fuzzy Syst. 37(8), 1–10 (2019)

    Google Scholar 

  32. G. Shikkenawis, S. Mitra, Image denoising using 2D orthogonal locality preserving discriminant projection. IET Image Proc. 14(3), 552–560 (2020)

    Article  Google Scholar 

  33. Y. Shin, M. Park, O. Lee, J. Kim, Deep orthogonal transform feature for image denoising. IEEE Access 8, 66898–66909 (2020)

    Article  Google Scholar 

  34. H. Talebi, P. Milanfar, Global image denoising. IEEE Trans. Image Process. 23(2), 755–768 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  35. Y. Tang, Y. Chen, N. Xu, A. Jiang, Image denoising via sparse approximation using eigenvectors of graph Laplacian. Digit. Signal Process. 50(C), 114–122 (2016)

    Article  Google Scholar 

  36. R. Verma, R. Pandey, Adaptive selection of search region for NLM based image denoising. Opt. Int. J. Light Electron Opt. 147, S0030402617309671 (2017)

    Article  Google Scholar 

  37. W. Waheed, D. Tay, Graph polynomial filter for signal denoising. IET Signal Proc. 12(3), 301–309 (2018)

    Article  Google Scholar 

  38. D. Wang, Y. Xiao, Y. Gao, Denoising method based on NSCT bivariate model and variational Bayes threshold estimation. Multim. Tools Appl. 78(7), 8927–8941 (2019)

    Article  Google Scholar 

  39. H. Wang, Y. Cen, Z. He, Z. He, R. Zhao, F. Zhang, Reweighted low-rank matrix analysis with structural smoothness for image denoising. IEEE Trans. Image Process. 27(4), 1777–1792 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  40. Y. Wu, L. Fang, S. Li, Weighted tensor rank-1 decomposition for nonlocal image denoising. IEEE Trans. Image Process. 28(6), 2719–2730 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  41. J. Xu, L. Zhang, D. Zhang, External prior guided internal prior learning for real-world noisy image denoising. IEEE Trans. Image Process. 27(6), 2996–3010 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  42. J. Xu, L. Zhang, D. Zhang A trilateral weighted sparse coding scheme for real-world image denoising. In: European Conference on Computer Vision, pp. 21–38 (2018)

  43. X. Yang, Y. Xu, Y. Quan, H. Ji, Image denoising via sequential ensemble learning. IEEE Trans. Image Process. 29, 5038–5049 (2020)

    Article  Google Scholar 

  44. Z. Yang, L. Fan, Y. Yang, Z. Yang, G. Gui, Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection. J. Frankl. Inst. Eng. Appl. Math. 356(16), 10138–10154 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  45. Z. Yang, Z. Yang, D. Han, Alternating direction method of multipliers for sparse and low-rank decomposition based on nonconvex nonsmooth weighted nuclear norm. IEEE Access 6, 56945–56953 (2018)

    Article  Google Scholar 

  46. A.C. Yağan, M.T. Özgen, Spectral graph based vertex-frequency Wiener filtering for image and graph signal denoising. IEEE Trans. Signal Inf. Process. Netw. 6, 226–240 (2020)

    MathSciNet  Google Scholar 

  47. H. Yue, X. Sun, J. Yang, F. Wu, Image denoising by exploring external and internal correlations. IEEE Trans. Image Process. 24(6), 1967–1982 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  48. X. Zeng, W. Bian, W. Liu, J. Shen, D. Tao, Dictionary pair learning on Grassmann manifolds for image denoising. IEEE Trans. Image Process. 24(11), 4556–4569 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  49. Z. Zha, X. Zhang, Q. Wang, Y. Bai, T. Lan, Group sparsity residual constraint for image denoising. Neurocomputing p. S0925231217317186 (2017)

  50. K. Zhang, W. Zuo, Y. Chen, D. Meng, L. Zhang, Beyond a Gaussian denoiser: residual learning of deep CNN for image denoising. IEEE Trans. Image Process. 26(7), 3142–3155 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  51. X. Zhang, J. Zheng, Y. Yan, L. Zhao, R. Jiang, Joint weighted tensor schatten \(p\)-norm and tensor \(l_p\)-norm minimization for image denoising. IEEE Access 7, 20273–20280 (2019)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant 61501169 and 81971289; Fundamental Research Funds for Central Universities of China under Grant B200202217.

Author information

Authors and Affiliations

  1. College of Internet of Things Engineering, Hohai University, Changzhou, 213022, China

    Yibin Tang, Jia Sun & Aimin Jiang

  2. School of Information Science and Technology, Southeast University, Nanjing, 210096, China

    Ying Chen & Lin Zhou

Authors
  1. Yibin Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jia Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Aimin Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ying Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lin Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yibin Tang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tang, Y., Sun, J., Jiang, A. et al. Adaptive Graph Filtering with Intra-Patch Pixel Smoothing for Image Denoising. Circuits Syst Signal Process 40, 5381–5400 (2021). https://doi.org/10.1007/s00034-021-01720-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-021-01720-x

Keywords

Search

Navigation