[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

A mixed model with multi-fidelity terms and nonlocal low rank regularization for natural image noise removal

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Reconstructing an original image from its corrupted observation is an important and fundamental problem in many image processing applications. Generally, the L1-norm or L2-norm combined with a regularization term (the total variation (TV), total generalized variation (TGV) or nuclear norm) is used to fit the impulse noise and Gaussian noise, respectively. However, these methods can only be used to remove a single type of noise from images, and traditional regularization terms often have difficulties in capturing some important prior knowledge of images, such as nonlocal self-similarity, low rank and sparsity. To overcome the above issues, we propose a mixed noise removal model with L1-L2 fidelity terms and a popular nonlocal low-rank regularization term, which has been shown to have more effective image denoising performance than traditional regularization methods. To solve this model, the split Bregman iteration method (SBIM) is adopted to decompose the difficult minimization optimization problem into four simple subproblems. Extensive experiments on natural images demonstrate that the effectiveness of the proposed method is better than that of other state-of-the-art methods.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Abiko R, Ikehara M (2019) Blind denoising of mixed gaussian-impulse noise by single cnn. In: ICASSP 2019-2019 IEEE International conference on acoustics, speech and signal processing (ICASSP). IEEE, pp 1717–1721

  2. Ahn B, Cho NI (2017) Block-matching convolutional neural network for image denoising, arXiv:1704.00524

  3. Alkinani MH, El-Sakka MR (2017) Patch-based models and algorithms for image denoising: a comparative review between patch-based images denoising methods for additive noise reduction. EURASIP J Image Video Process 2017(1):1–27

    Google Scholar 

  4. Bovik AC (2010) Handbook of image and video processing. Academic press

  5. Buades A, Coll B, Morel JM (2005) A non-local algorithm for image denoising. In: IEEE Computer society conference on computer vision and pattern recognition

  6. Bredies K, Kunisch K, Pock T (2010) Total generalized variation. SIAM J Imaging Sci 3(3):492–526

    MathSciNet  MATH  Google Scholar 

  7. Burger HC, Schuler CJ, Harmeling S (2012) Image denoising with multi-layer perceptrons, part 1: comparison with existing algorithms and with bounds, arXiv:1211.1544

  8. Cai J-F, Chan R, Nikolova M (2008) Two-phase approach for deblurring images corrupted by impulse plus gaussian noise. Inverse Probl Imaging 2 (2):187–204

    MathSciNet  MATH  Google Scholar 

  9. Cai J-F, Candès EJ, Shen Z (2010) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982

    MathSciNet  MATH  Google Scholar 

  10. Cai X, Chan R, Zeng T (2013) A two-stage image segmentation method using a convex variant of the mumford–shah model and thresholding. SIAM J Imaging Sci 6(1):368–390

    MathSciNet  MATH  Google Scholar 

  11. Chambolle A (2004) An algorithm for total variation minimization and applications. J Math Imaging Vis 20(1-2):89–97

    MathSciNet  MATH  Google Scholar 

  12. Chambolle A, Pock T (2011) A first-order primal-dual algorithm for convex problems with applications to imaging. J Math Imaging Vis 40(1):120–145

    MathSciNet  MATH  Google Scholar 

  13. Chatterjee P, Milanfar P (2009) Clustering-based denoising with locally learned dictionaries. IEEE Trans Image Process 18(7):1438–1451

    MathSciNet  MATH  Google Scholar 

  14. Deng L-J, Feng M, Tai X-C (2019) The fusion of panchromatic and multispectral remote sensing images via tensor-based sparse modeling and hyper-laplacian prior. Inf Fusion 52:76–89

    Google Scholar 

  15. Dong W, Xin L, Lei Z, Shi G (2011) Sparsity-based image denoising via dictionary learning and structural clustering. In: Computer vision & pattern recognition

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

    MathSciNet  MATH  Google Scholar 

  17. Dong W, Shi G, Li X, Ma Y, Huang F (2014) Compressive sensing via nonlocal low-rank regularization. IEEE Trans Image Process 23(8):3618–3632

    MathSciNet  MATH  Google Scholar 

  18. Duval V, Aujol J-F, Gousseau (2010) On the parameter choice for the non-local means

  19. Eckart C, Young G (1936) The approximation of one matrix by another of lower rank. Psychometrika 1(3):211–218

    MATH  Google Scholar 

  20. Ferstl D, Reinbacher C, Ranftl R, Rüther M, Bischof H (2013) Image guided depth upsampling using anisotropic total generalized variation. In: Proceedings of the IEEE International Conference on Computer Vision, pp 993–1000

  21. Froment J (2014) Parameter-free fast pixelwise non-local means denoising. Image Process Line 4:300–326

    Google Scholar 

  22. Goldstein T, Osher S (2009) The split bregman method for l1-regularized problems. SIAM J Imaging Sci 2(2):323–343

    MathSciNet  MATH  Google Scholar 

  23. He B, Yang H, Wang S (2000) Alternating direction method with self-adaptive penalty parameters for monotone variational inequalities. J Optim Theory Appl 106(2):337–356

    MathSciNet  MATH  Google Scholar 

  24. He B, Tao M, Yuan X (2012) Alternating direction method with gaussian back substitution for separable convex programming. SIAM J Optim 22 (2):313–340

    MathSciNet  MATH  Google Scholar 

  25. Hebert T, Leahy R (1989) A generalized em algorithm for 3-d bayesian reconstruction from poisson data using gibbs priors. IEEE Trans Med Imaging 8(2):194–202

    Google Scholar 

  26. Huang T, Dong W, Xie X, Shi G, Bai X (2017) Mixed noise removal via laplacian scale mixture modeling and nonlocal low-rank approximation. IEEE Trans Image Process 26(7):3171–3186

    MathSciNet  MATH  Google Scholar 

  27. Ji H, Huang S, Shen Z, Xu Y (2011) Robust video restoration by joint sparse and low rank matrix approximation. SIAM J Imaging Sci 4(4):1122–1142

    MathSciNet  MATH  Google Scholar 

  28. Jia T, Shi Y, Zhu Y, Wang L (2016) An image restoration model combining mixed l1/l2 fidelity terms. J Vis Commun Image Represent 38:461–473

    Google Scholar 

  29. Jiang J, Zhang L, Yang J (2014) Mixed noise removal by weighted encoding with sparse nonlocal regularization. IEEE Trans Image Process 23(6):2651–2662

    MathSciNet  MATH  Google Scholar 

  30. Jiang J, Yang J, Cui Y, Luo L (2015) Mixed noise removal by weighted low rank model. Neurocomputing 151:817–826

    Google Scholar 

  31. Jung M (2015) Kang Simultaneous cartoon and texture image restoration with higher-order regularization. SIAM J Imaging Sci 8(1):721–756

    MathSciNet  MATH  Google Scholar 

  32. Jung M (2017) Piecewise-smooth image segmentation models with [formula] data-fidelity terms. J Sci Comput 70(3):1229–1261

    MathSciNet  MATH  Google Scholar 

  33. Jung M, Kang M (2015) Efficient nonsmooth nonconvex optimization for image restoration and segmentation. J Sci Comput 62(2):336–370

    MathSciNet  MATH  Google Scholar 

  34. Knoll F, Bredies K, Pock T, Stollberger R (2011) Second order total generalized variation (tgv) for mri. Magn Reson Med 65(2):480–491

    Google Scholar 

  35. Kostadin D, Alessandro F, Vladimir K, Karen E (2007) Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095

    MathSciNet  Google Scholar 

  36. Lan X, Roth S, Huttenlocher D, Black MJ (2006) Efficient belief propagation with learned higher-order markov random fields. In: European conference on computer vision. Springer, pp 269–282

  37. Liao X, Li K, Yin J (2017) Separable data hiding in encrypted image based on compressive sensing and discrete fourier transform. Multimed Tools Appl 76(20):20739–20753

    Google Scholar 

  38. Liao X, Yu Y, Li B, Li Z, Qin Z (2019) A new payload partition strategy in color image steganography. IEEE Transactions on Circuits and Systems for Video Technology

  39. Mahmoudi M, Sapiro G (2005) Fast image and video denoising via nonlocal means of similar neighborhoods. IEEE Signal Process Lett 12(12):839–842

    Google Scholar 

  40. Mairal J, Bach F, Ponce J, Sapiro G, Zisserman A (2010) Non-local sparse models for image restoration. In: IEEE International conference on computer vision

  41. Michael E, Michal A (2006) Image denoising via sparse and redundant representations over learned dictionaries. IEEE Tip 15(12):3736–3745

    MathSciNet  Google Scholar 

  42. Milovic C, Bilgic B, Zhao B, Acosta-Cabronero J, Tejos C (2018) Fast nonlinear susceptibility inversion with variational regularization. Magn Reson Med 80(2):814–821

    Google Scholar 

  43. Mohan J, Krishnaveni V, Guo Y (2014) A survey on the magnetic resonance image denoising methods. Biomed Signal Processing Control 9:56–69

    Google Scholar 

  44. Osher S, Wang B, Yin P, Luo X, Barekat F, Pham M, Lin A (2018) Laplacian smoothing gradient descent, arXiv:1806.06317

  45. Qin Z, Goldfarb D, Ma S (2015) An alternating direction method for total variation denoising. Optim Methods Softw 30(3):594–615

    MathSciNet  MATH  Google Scholar 

  46. Rudin LI, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1-4):259–268

    MathSciNet  MATH  Google Scholar 

  47. Srebro N, Jaakkola T (2003) Weighted low-rank approximations. In: Proceedings of the 20th International Conference on Machine Learning (ICML-03), pp 720–727

  48. Tihonov AN (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math 4:1035–1038

    MathSciNet  Google Scholar 

  49. Wang Y, Yang J, Yin W, Zhang Y (2008) A new alternating minimization algorithm for total variation image reconstruction. SIAM J Imaging Sci 1 (3):248–272

    MathSciNet  MATH  Google Scholar 

  50. Wang F, Huang H, Liu J (2019) Variational based mixed noise removal with cnn deep learning regularization. IEEE Transactions on Image Processing

  51. Weisheng D, Guangming S, Xin L (2013) Nonlocal image restoration with bilateral variance estimation: a low-rank approach. IEEE Trans Image Process 22(2):700–711

    MathSciNet  MATH  Google Scholar 

  52. Xiao Y, Zeng T, Yu J, Ng MK (2011) Restoration of images corrupted by mixed gaussian-impulse noise via l1–l0 minimization. Pattern Recogn 44 (8):1708–1720

    MATH  Google Scholar 

  53. Xie Y, Gu S, Liu Y, Zuo W, Zhang W, Zhang L (2016) Weighted schatten p-norm minimization for image denoising and background subtraction. IEEE Trans Image Process 25(10):4842–4857

    MathSciNet  MATH  Google Scholar 

  54. Xiong B, Yin Z (2011) A universal denoising framework with a new impulse detector and nonlocal means. IEEE Trans Image Process 21(4):1663–1675

    MathSciNet  MATH  Google Scholar 

  55. Yan M (2013) Restoration of images corrupted by impulse noise and mixed gaussian impulse noise using blind inpainting. SIAM J Imaging Sci 6(3):1227–1245

    MathSciNet  MATH  Google Scholar 

  56. Yang Y, Sun J, Li H, Xu Z (2017) Admm-net: A deep learning approach for compressive sensing mri. corr, arXiv:1705.06869

  57. Yang J, Zhang Y, Yin W (2009) An efficient tvl1 algorithm for deblurring multichannel images corrupted by impulsive noise. SIAM J Sci Comput 31(4):2842–2865

    MathSciNet  MATH  Google Scholar 

  58. Zhang Y (2010) An alternating direction algorithm for nonnegative matrix factorization, Technical Report

  59. Zhang D, Hu Y, Ye J, Li X, He X (2012) Matrix completion by truncated nuclear norm regularization. In: 2012 IEEE Conference on computer vision and pattern recognition. IEEE, pp 2192–2199

  60. 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

    MathSciNet  MATH  Google Scholar 

  61. Zhang K, Zuo W, Gu S, Zhang L (2017) Learning deep cnn denoiser prior for image restoration. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 3929–3938

  62. Zhou T, Bhaskar H, Liu F, Yang J, Cai P (2017) Online learning and joint optimization of combined spatial-temporal models for robust visual tracking. Neurocomputing 226:221–237

    Google Scholar 

  63. Zhou W, Zhang Y, Liu Y (2017) Matrix-value linear regression for image denoising. DEStech Transactions on Computer Science and Engineering, no. mmsta

  64. Zhou T, Liu F, Bhaskar H, Yang J (2018) Robust visual tracking via online discriminative and low-rank dictionary learning. IEEE Trans Cybern 48 (9):2643–2655

    Google Scholar 

  65. Zhou T, Thung K-H, Liu M, Shen D (2019) Brain-wide genome-wide association study for alzheimer’s disease via joint projection learning and sparse regression model. IEEE Trans Biomed Eng 66(1):165–175

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Network Information Center, Chinese Academy of Sciences, Beijing, 100190, China

    Yuepeng Li & Chun Li

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Yuepeng Li & Chun Li

Authors
  1. Yuepeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuepeng Li.

Additional information

Publisher’s note

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

Appendix: Demo parameters selection process for GN0.01 noise removal

Appendix: Demo parameters selection process for GN0.01 noise removal

Table 5
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Y., Li, C. A mixed model with multi-fidelity terms and nonlocal low rank regularization for natural image noise removal. Multimed Tools Appl 79, 33043–33069 (2020). https://doi.org/10.1007/s11042-020-09565-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09565-3

Keywords

Search

Navigation