Skip to main content
SpringerLink
Log in

An Effective Weighted Hybrid Regularizing Approach for Image Noise Reduction

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

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

Digital images are mostly noised due to transmission and capturing disturbances. Hence, denoising becomes a notable issue because of the necessity of removing noise before its use in any application. In denoising, the important challenge is to remove the noise while protecting true information and avoiding undesirable modification in the images. The performance of classical denoising methods including convex total variation or some nonconvex regularizers is not effective enough. Thus, it is still an ongoing research toward better denoising result. Since edge preservation is a tricky issue during denoising process, designing an appropriate regularizer for a given fidelity is a mostly crucial matter in real-world problems. Therefore, we attempt to design a robust smoothing term in energy functional so that it can reduce the possibility of discontinuity and distortion of image edge details. In this work, we introduce a new denoising technique that inherits the benefits of both convex and nonconvex regularizers. The proposed method encompasses with a novel weighted hybrid regularizer in variational framework to ensure a better trade-off between the noise removal and image edge preservation. A new algorithm based on Chambolle’s method and iteratively reweighting method is proposed to solve the model efficiently. The numerical results ensure that the proposed hybrid denoising approach can perform better than the classical convex, nonconvex regularizer-based denoising and some other methods.

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
Fig. 6

Similar content being viewed by others

References

  1. A. Aboshosha, M. Hassan, M. Ashour, M. El Mashade, Image denoising based on spatial filters, an analytical study, in 2009 International Conference on Computer Engineering & Systems (IEEE, 2009), pp. 245–250

  2. H. Al-Marzouqi, G. AlRegib, Curvelet transform with learning-based tiling. Signal Process. Image Commun. 53, 24–39 (2017)

    Article  Google Scholar 

  3. G. Aubert, P. Kornprobst, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Springer, Berlin, 2006)

    Book  MATH  Google Scholar 

  4. G. Aubert, L. Vese, A variational method in image recovery. SIAM J. Numer. Anal. 34(5), 1948–1979 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Baloch, H. Ozkaramanli, Image denoising via correlation-based sparse representation. Signal Image Video Process. 11, 1501–1508 (2017)

    Article  Google Scholar 

  6. K. Bredies, Y. Dong, M. Hintermüller, Spatially dependent regularization parameter selection in total generalized variation models for image restoration. Int. J. Comput. Math. 90(1), 109–123 (2013)

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  8. A. Chambolle, P.-L. Lions, Image recovery via total variation minimization and related problems. Numer. Math. 76(2), 167–188 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  9. F. Chen, Y. Jiao, L. Lin, Q. Qin, Image deblurring via combined total variation and framelet. Circuits Syst. Signal Process. 33(6), 1899–1916 (2014)

    Article  Google Scholar 

  10. Q. Chen, Q. Sun, D. Xia, Homogeneity similarity based image denoising. Pattern Recognit. 43(12), 4089–4100 (2010)

    Article  MATH  Google Scholar 

  11. N. Chumchob, K. Chen, C. Brito-Loeza, A new variational model for removal of combined additive and multiplicative noise and a fast algorithm for its numerical approximation. Int. J. Comput. Math. 90(1), 140–161 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  12. C. Couprie, L. Grady, H. Talbot, L. Najman, Combinatorial continuous maximum flow. SIAM J. Imaging Sci. 4(3), 905–930 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. W. Cheng, K. Hirakawa, Minimum risk wavelet shrinkage operator for Poisson image denoising. IEEE Trans. Image Process. 24(5), 1660–1671 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  14. 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 

  15. E. Ehsaeyan, A new shearlet hybrid method for image denoising. Iran. J. Electr. Electron. Eng. 12(2), 97–104 (2016)

    Google Scholar 

  16. M. Elad, M. Aharon, Image denoising via sparse and redundant representations over learned dictionaries. IEEE Trans. Image Process. 15(12), 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  17. A. Fathi, A.R. Naghsh-Nilchi, Efficient image denoising method based on a new adaptive wavelet packet thresholding function. IEEE Trans. Image Process. 21(9), 3981–3990 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  18. V. Fedorov, C. Ballester, Affine non-local means image denoising. IEEE Trans. Image Process. 26(5), 2137–2148 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. M. Frandes, I.E. Magnin, R. Prost, Wavelet thresholding-based denoising method of list-mode MLEM algorithm for compton imaging. IEEE Trans. Nucl. Sci. 58(3), 714–723 (2011)

    Article  Google Scholar 

  20. S. Gai, B. Zhang, C. Yang, Y. Lei, Speckle noise reduction in medical ultrasound image using monogenic wavelet and Laplace mixture distribution. Digit. Signal Process. 72, 192–207 (2018)

    Article  Google Scholar 

  21. S. Gai, Y. Zhang, C. Yang, L. Wang, J. Zhou, Color monogenic wavelet transform for multichannel image denoising. Multidimens. Syst. Signal Process. 28(4), 1463–1480 (2017)

    Article  MathSciNet  Google Scholar 

  22. P. Getreuer, Rudin–Osher–Fatemi total variation denoising using split Bregman. Image Process. Line 2, 74–95 (2012)

    Article  Google Scholar 

  23. M. Giaquinta, S. Hildebrandt, Calculus of Variations I. Grundlehren der mathematischen Wissenschaften, vol. 310 (Springer, Berlin, 2004)

    Google Scholar 

  24. G. Gilboa, S. Osher, Nonlocal operators with applications to image processing. Multiscale Model. Simul. 7(3), 1005–1028 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  25. T. Goldstein, S. Osher, The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. X. Guo, C. Meng, Research on support vector machine in image denoising. Int. J. Signal Process. Image Process. Pattern Recognit. 8(2), 19–28 (2015)

    Google Scholar 

  27. A.B. Hamza, P.L. Luque-Escamilla, J. Martínez-Aroza, R. Román-Roldán, Removing noise and preserving details with relaxed median filters. J. Math. Imaging Vis. 11(2), 161–177 (1999)

    Article  MathSciNet  Google Scholar 

  28. Y. Han, X.-C. Feng, G. Baciu, W.-W. Wang, Nonconvex sparse regularizer based speckle noise removal. Pattern Recogn. 46(3), 989–1001 (2013)

    Article  Google Scholar 

  29. Y. Han, C. Xu, G. Baciu, A variational based smart segmentation model for speckled images. Neurocomputing 178, 62–70 (2016)

    Article  Google Scholar 

  30. Y. Han, C. Xu, G. Baciu, X. Feng, Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer. Int. J. Comput. Math. 91(10), 2243–2259 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  31. Y. Han, C. Xu, G. Baciu, M. Li, M.R. Islam, Cartoon and texture decomposition-based color transfer for fabric images. IEEE Trans. Multimed. 19(1), 80–92 (2017)

    Article  Google Scholar 

  32. Y. Hancheng, L. Zhao, H. Wang, Image denoising using trivariate shrinkage filter in the wavelet domain and joint bilateral filter in the spatial domain. IEEE Trans. Image Process. 18(10), 2364–2369 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  33. R. Harrabi, E. Ben Braiek, Isotropic and anisotropic filtering techniques for image denoising: a comparative study with classification, in 2012 16th IEEE Mediterranean Electrotechnical Conference (IEEE, 2012), pp. 370–374

  34. F. Heide, S. Diamond, M. Nießner, J. Ragan-Kelley, W. Heidrich, G. Wetzstein, ProxImaL. ACM Trans. Graph. 35(4), 1–15 (2016)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  36. K.-W. Hung, W.-C. Siu, Single-image super-resolution using iterative Wiener filter based on nonlocal means. Signal Process. Image Commun. 39, 26–45 (2015)

    Article  Google Scholar 

  37. J. Ho, W.-L. Hwang, Wavelet Bayesian network image denoising. IEEE Trans. Image Process. 22(4), 1277–1290 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  38. M.R. Islam, C. Xu, Y. Han, R.A.R. Ashfaq, A novel weighted variational model for image denoising. Int. J. Pattern Recognit. Artif. Intell. 31(12) (2017). https://doi.org/10.1142/S0218001417540222

  39. Y. Kuang, L. Zhang, Z. Yi, Image denoising via sparse dictionaries constructed by subspace learning. Circuits Syst. Signal Process. 33(7), 2151–2171 (2014)

    Article  Google Scholar 

  40. J. Liua, C. Shi, M. Gao, Image denoising based on BEMD and PDE, in 2011 3rd International Conference on Computer Research and Development (IEEE, 2011), pp. 110–112

  41. A. Li, D. Chen, K. Lin, G. Sun, Nonlocal joint regularizations framework with application to image denoising. Circuits Syst. Signal Process. 35(8), 2932–2942 (2016)

    Article  Google Scholar 

  42. A. Li, D. Chen, G. Sun, K. Lin, Sparse representation-based image restoration via nonlocal supervised coding. Opt. Rev. 23(5), 776–783 (2016)

    Article  Google Scholar 

  43. H. Liu, R. Xiong, J. Zhang, W. Gao, Image denoising via adaptive soft-thresholding based on non-local samples, in 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2015), pp. 484–492

  44. P. Liu, L. Xiao, J. Zhang, A fast higher degree total variation minimization method for image restoration. Int. J. Comput. Math. 93(8), 1383–1404 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  45. X.Y. Liu, C.-H. Lai, K.A. Pericleous, A fourth-order partial differential equation denoising model with an adaptive relaxation method. Int. J. Comput. Math. 92(3), 608–622 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  46. C.-W. Lu, Image restoration and decomposition using non-convex non-smooth regularisation and negative Hilbert–Sobolev norm. IET Image Process. 6(6), 706–716 (2012)

    Article  MathSciNet  Google Scholar 

  47. J. Lu, K. Qiao, L. Shen, Y. Zou, Fixed-point algorithms for a TVL1 image restoration model. Int. J. Comput. Math. (2017). https://doi.org/10.1080/00207160.2017.1343470

  48. J. Ma, X. Fan, S.X. Yang, X. Zhang, X. Zhu, Contrast limited adaptive histogram equalization-based fusion in YIQ and HSI color spaces for underwater image enhancement. Int. J. Pattern Recognit. Artif. Intell. 32(07), 1854018 (2018)

    Article  Google Scholar 

  49. K. Mechlem, S. Allner, K. Mei, F. Pfeiffer, P.B. Noël, Dictionary-based image denoising for dual energy computed tomography, in Proceedings SPIE 9783, Medical Imaging: Physics of Medical Imaging (2016), p. 97830E. https://doi.org/10.1117/12.2216749

  50. J. Mejia, B. Mederos, R.A. Mollineda, L.O. Maynez, Noise reduction in small animal PET images using a variational non-convex functional. IEEE Trans. Nucl. Sci. 63(5), 2577–2585 (2016)

    Article  Google Scholar 

  51. M.K. Ng, L. Qi, Y. Yang, Y. Huang, On semismooth newton’s methods for total variation minimization. J. Math. Imaging Vis. 27(3), 265–276 (2007)

    Article  MathSciNet  Google Scholar 

  52. X. Nie, H. Qiao, B. Zhang, X. Huang, A nonlocal TV-based variational method for PolSAR data speckle reduction. IEEE Trans. Image Process. 25(6), 2620–2634 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  53. M. Nikolova, M.K. Ng, C.-P. Tam, Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction. IEEE Trans. Image Process. 19(12), 3073–3088 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  54. P. Ochs, A. Dosovitskiy, T. Brox, T. Pock, On iteratively reweighted algorithms for nonsmooth nonconvex optimization in computer vision. SIAM J. Imaging Sci. 8(1), 331–372 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  55. S.J. Padmagireeshan, R.C. Johnson, A.A. Balakrishnan, V. Paul, A.V. Pillai, A.A. Raheem, Performance analysis of magnetic resonance image denoising using contourlet transform, in 2013 Third International Conference on Advances in Computing and Communications (IEEE, 2013), pp. 396–399

  56. S.M.M. Rahman, M.O. Ahmad, M.N.S. Swamy, Bayesian wavelet-based image denoising using the Gauss–Hermite expansion. IEEE Trans. Image Process. 17(10), 1755–1771 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  57. V.N.P. Raj, T. Venkateswarlu, Denoising of medical images using undecimated wavelet transform, in 2011 IEEE Recent Advances in Intelligent Computational Systems (IEEE, 2011), pp. 483–488

  58. N. Rajpoot, I. Butt, A multiresolution framework for local similarity based image denoising. Pattern Recognit. 45(8), 2938–2951 (2012)

    Article  Google Scholar 

  59. A. Ranjbaran, A.H.A. Hassan, M. Jafarpour, B. Ranjbaran, A Laplacian based image filtering using switching noise detector. SpringerPlus 4(1), 119 (2015)

    Article  Google Scholar 

  60. L.I. Rudin, S. Osher, E. Fatemi, Nonlinear total variation based noise removal algorithms. Physica D 60(1), 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  61. L.I. Rudin, S. Osher, Total variation based image restoration with free local constraints, in Proceedings of 1st International Conference on Image Processing, vol. 1 (IEEE Computer Society Press, 1994), pp. 31–35

  62. C.H. Seng, A. Bouzerdoum, M.G. Amin, S.L. Phung, Two-stage fuzzy fusion with applications to through-the-wall radar imaging. IEEE Geosci. Remote Sens. Lett. 10(4), 687–691 (2013)

    Article  Google Scholar 

  63. H. Scharr, H. Spies, Accurate optical flow in noisy image sequences using flow adapted anisotropic diffusion. Signal Process. Image Commun. 20(6), 537–553 (2005)

    Article  Google Scholar 

  64. Y. Shen, Q. Liu, S. Lou, Y.-L. Hou, Wavelet-based total variation and nonlocal similarity model for image denoising. IEEE Signal Process. Lett. 24(6), 877–881 (2017)

    Article  Google Scholar 

  65. V.B. Surya Prasath, D. Vorotnikov, R. Pelapur, S. Jose, G. Seetharaman, K. Palaniappan, Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent. IEEE Trans. Image Process. 24(12), 5220–5235 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  66. C. Sutour, C.-A. Deledalle, J.-F. Aujol, Adaptive regularization of the NL-means: application to image and video denoising. IEEE Trans. Image Process. 23(8), 3506–3521 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  67. A.N. Tikhonov, V.Y. Arsenin, Solutions of Ill-Posed Problems, 1st edn. (Winston, Washington, 1977)

    MATH  Google Scholar 

  68. Z. Tu, W. Xie, J. Cao, C. van Gemeren, R. Poppe, R.C. Veltkamp, Variational method for joint optical flow estimation and edge-aware image restoration. Pattern Recognit. 65, 11–25 (2017)

    Article  Google Scholar 

  69. T. Veerakumar, R.P.K. Jagannath, B.N. Subudhi, S. Esakkirajan, Impulse noise removal using adaptive radial basis function interpolation. Circuits Syst. Signal Process. 36(3), 1192–1223 (2017)

    Article  Google Scholar 

  70. C. Wang, J. Zhou, S. Liu, Adaptive non-local means filter for image deblocking. Signal Process. Image Commun. 28(5), 522–530 (2013)

    Article  Google Scholar 

  71. D. Wang, J. Gao, An improved noise removal model based on nonlinear fourth-order partial differential equations. Int. J. Comput. Math. 93(6), 942–954 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  72. X. Wang, H. Wang, J. Yang, Y. Zhang, A new method for nonlocal means image denoising using multiple images. PLoS ONE 11(7), 1–9 (2016)

    Google Scholar 

  73. X. Xu, T. Bu, An adaptive parameter choosing approach for regularization model. Int. J. Pattern Recognit. Artif. Intell. 32, 1859013 (2018)

    Article  Google Scholar 

  74. R. Yan, L. Shao, Y. Liu, Nonlocal hierarchical dictionary learning using wavelets for image denoising. IEEE Trans. Image Process. 22(12), 4689–4698 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  75. G.-D. Zhang, X.-H. Yang, H. Xu, D.-Q. Lu, Y.-X. Liu, Image denoising based on support vector machine, in 2012 Spring Congress on Engineering and Technology (IEEE, 2012), pp. 1–4

  76. K.S. Zhang, L. Zhong, X.Y. Zhang, Image restoration via group l2,1 norm-based structural sparse representation. Int. J. Pattern Recognit. Artif. Intell. 32(04), 1854008 (2018)

    Article  MathSciNet  Google Scholar 

  77. M. Zhu, S.J. Wright, T.F. Chan, Duality-based algorithms for total-variation-regularized image restoration. Comput. Optim. Appl. 47(3), 377–400 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  78. Z. Zuo, W.D. Yang, X. Lan, L. Liu, J. Hu, L. Yan, Adaptive nonconvex nonsmooth regularization for image restoration based on spatial information. Circuits Syst. Signal Process. 33(8), 2549–2564 (2014)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61402290, 61472257, 61772343 and 61379030; in part by the Foundation for Distinguished Young Talents in Higher Education of Guangdong, China, under Grant 2014KQNCX134; in part by the Natural Science Foundation of Guangdong, China, under Grant 1714050003822; and in part by the Science Foundation of Shenzhen Science Technology and Innovation Commission, China, under Grant JCYJ20160331114526190.

Author information

Authors and Affiliations

  1. College of Computer Science and Software Engineering, Shenzhen University, Shenzhen, 518060, China

    Md. Robiul Islam & Rana Aamir Raza

  2. College of Mathematics and Computational Science, Shenzhen University, Shenzhen, 518060, China

    Chen Xu & Yu Han

Authors
  1. Md. Robiul Islam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chen Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rana Aamir Raza
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yu Han
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chen Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Islam, M.R., Xu, C., Raza, R.A. et al. An Effective Weighted Hybrid Regularizing Approach for Image Noise Reduction. Circuits Syst Signal Process 38, 218–241 (2019). https://doi.org/10.1007/s00034-018-0853-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0853-1

Keywords

Search

Navigation