Skip to main content
Log in

Denoising of natural images through robust wavelet thresholding and genetic programming

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Digital images play an essential role in analysis tasks that can be applied in various knowledge domains, including medicine, meteorology, geology, and biology. Such images can be degraded by noise during the process of acquisition, transmission, storage, or compression. The use of local filters in image restoration may generate artifacts when these filters are not well adapted to the image content as a result of the heuristic optimization of local filters. Denoising methods based on learning procedure are more capable than parametric filters for addressing the conflicts between noise suppression and artifact reduction. In this study, we present a nonlinear filtering method based on a two-step switching scheme to remove both salt-and-pepper and additive white Gaussian noises. In the switching scheme, two cascaded detectors are used to detect noise, and two corresponding estimators are employed to effectively and efficiently filter the noise in an image. In the process of training, a method according to patch clustering is utilized, and genetic programming (GP) is subsequently applied to determine the optimum filter (wavelet-domain filter) for each individual cluster, while in testing part, the optimum filter trained beforehand by GP is recovered and used on the inputted corrupted patch. This adaptive structure is employed to cope with several noise types. Experimental and comparative analysis results show that the denoising performance of the proposed method is superior to that of existing denoising methods as per both quantitative and qualitative assessments.

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

Access this article

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
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Notes

  1. http://gp-lab.sourceforrge.net/download.html

References

  1. Gonzalez, R., Woods, R.: Digital Image Processing. Pearson Prentice Hall, Upper Saddle River (2008)

    Google Scholar 

  2. Jain, P., Tyagi, V.: Spatial and frequency domain filters for restoration of noisy images. IETE J. Edu. 54(2), 108–116 (2013)

    Article  Google Scholar 

  3. Khmag, A., Ramli, A., Hashim, S., Al-Haddad, S.A.R.: Additive noise reduction in natural images using second-generation wavelet transform hidden Markov models. IEEJ Trans. Electr. Electron. Eng. 11(3), 257–265 (2015)

    Google Scholar 

  4. Buades, A., Coll, B., Morel, J.-M.: A non-local algorithm for image denoising. IEEE Conf. Comput. Soc. Comput. Vis. Pattern Recognit. 2, 60–65 (2005)

    MATH  Google Scholar 

  5. Ko, S.-J., Lee, Y.H.: Center weighted median filters and their applications to image enhancement. IEEE Trans. Circuits Syst. 38(9), 984–993 (1991)

    Article  Google Scholar 

  6. Li, Y., Wei, H.-L., Billings, S.A.: Identification of time-varying systems using multi-wavelet basis functions. IEEE Trans. Control Syst. Technol. 19(3), 656–663 (2011)

    Article  Google Scholar 

  7. Le, Y., Wei, H.-L., Billings, S.A., Liao, X-f: Time-varying linear and nonlinear parametric model for Granger causality analysis. Phys. Rev. E. 85(4), 1–8 (2012)

    Google Scholar 

  8. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(7), 629–639 (1990)

    Article  Google Scholar 

  9. Rudin, L., Osher, S.: Total variation based image restoration with free local constraints. IEEE Int. Conf. Image Process. 1, 31–35 (1994)

    Article  Google Scholar 

  10. Porikli, F.: Constant time O (1) bilateral filtering. In: IEEE conference on computer vision and pattern recognition. pp. 1–8 (2008)

  11. Jain, P., Tyagi, V.: An adaptive edge-preserving image denoising technique using tetrolet transforms. Vis. Comput. 31(5), 657–674 (2014)

    Article  Google Scholar 

  12. Shapiro, L., Stockman, G.C.: Computer Vision. Prentice Hall, Upper Saddle River (2001)

    Google Scholar 

  13. Smith, S.M., Brady, J.M.: SUSAN-a new approach to low level image processing. Int. J. Comput. Vis. 23(1), 45–78 (1997)

    Article  Google Scholar 

  14. Shao, L., Zhang, H., De Haan, G.: An overview and performance evaluation of classification-based least squares trained filters. IEEE Trans. Image Process. 17(10), 1772–1782 (2008)

    Article  MathSciNet  Google Scholar 

  15. Liu, Q., Zhang, C., Guo, Q., Xu, H., Zhou, Y.: Adaptive sparse coding on PCA dictionary for image denoising. Vis. Comput. 32(4), 535–549 (2015)

    Article  Google Scholar 

  16. Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  17. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Process. 16(8), 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  18. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: BM3D image denoising with shape-adaptive principal component analysis. In: Processidng of SPARS’09-signal processing with adaptive sparse structured representations, pp. 1–6 (2009)

  19. Wongsawat, Y., Rao, K., Oraintara, S.: Multichannel SVD-based image de-noising. IEEE Int. Symp. Circuits Syst. 6, 5990–5993 (2005)

    Article  Google Scholar 

  20. Orchard, J., Ebrahimi, M., Wong, A.: Efficient nonlocal-means denoising using the SVD. In: IEEE international conference on image processing, pp 1732–1735 (2008)

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

    Article  MathSciNet  Google Scholar 

  22. Bouboulis, P., Slavakis, K., Theodoridis, S.: Adaptive kernel-based image denoising employing semi-parametric regularization. IEEE Trans. Image Proc. 19(6), 1465–1479 (2010)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  24. Yan, R., Shao, L. (eds.) Image blur classification and parameter identification using two-stage deep belief networks. British machine vision conference (BMVC), Bristol, UK (2013)

  25. Dong, W., Zhang, L., Shi, G., Wu, X.: Image deblurring and super-resolution by adaptive sparse domain selection and adaptive regularization. IEEE Trans. Image Process. 20(7), 1838–1857 (2011)

    Article  MathSciNet  Google Scholar 

  26. Petrović, N., Crnojević, V.: Impulse noise detection based on robust statistics and genetic programming. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds.) Advanced Concepts for Intelligent Vision Systems, vol. 3708, pp. 643–649. Springer, Berlin (2005)

  27. Petrović, N.I., Crnojević, V.S.: Evolutionary tree-structured filter for impulse noise removal. In: Blanc-Talon, J., Philips, W., Popescu, D., Scheunders, P. (eds.) Advanced Concepts for Intelligent Vision Systems, Vol. 4179, pp. 103–113. Springer, Berlin (2006)

  28. Krommweh, J.: Tetrolet transform: a new adaptive Haar wavelet algorithm for sparse image representation. J. Vis. Commun. Image Represent. 21(4), 364–374 (2010)

    Article  Google Scholar 

  29. Isgrò, F., Tegolo, D.: A distributed genetic algorithm for restoration of vertical line scratches. Parallel Comput. 34(12), 727–734 (2008)

    Article  Google Scholar 

  30. Korürek, M., Yüksel, A., Iscan, Z., Dokur, Z., Ölmez, T.: Retrospective correction of near field effect of X-ray source in radiographic images by using genetic algorithms. Expert Syst. Appl. 37(3), 1946–1954 (2010)

    Article  Google Scholar 

  31. Petrović, N., Crnojević, V.: Universal impulse noise filter based on genetic programming. IEEE Trans. Image Process. 17(7), 1109–1120 (2008)

    Article  MathSciNet  Google Scholar 

  32. Zhang, S., Karim, M.A.: A new impulse detector for switching median filters. IEEE Signal Process. Lett. 9(11), 360–363 (2002)

    Article  Google Scholar 

  33. Chan, R.H., Ho, C.-W., Nikolova, M.: Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Trans. Image Proc. 14(10), 1479–1485 (2005)

    Article  Google Scholar 

  34. Yan, R., Shao, L., Liu, L., Liu, Y.: Natural image denoising using evolved local adaptive filters. Signal Process 103, 36–44 (2014)

    Article  Google Scholar 

  35. Kim, E.Y., Kim, K.-T., Kim, B.: Genetic algorithm-based reconstruction of old films corrupted by scratches and blotches. Pattern Recognit. Lett. 34(2), 226–237 (2013)

    Article  Google Scholar 

  36. Khmag, A., Ramli, A., Al Haddad, S.: Design of natural image denoising filter based on second-generation wavelet transformation and principle component analysis. J. Med. Imaging Health Inform. 5(6), 1261–1266 (2015)

    Article  Google Scholar 

  37. Koza, J.R.: Genetic programming II: Automatic Discovery of Reusable Programs. MIT Press, A Bradford Book, Cambridge (1994)

  38. Liu, Y.: Image denoising method based on threshold, wavelet transform and genetic algorithm. Int. J. Signal Process. Image Process. Pattern Recognit. 8(2), 29–40 (2015)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  40. Thaipanich, T., Oh, B.T., Wu, P., Xu, D., Kuo, C.: Improved image denoising with adaptive nonlocal means (ANL-means) algorithm. IEEE Trans. Consum. Electron. 56(4), 2623–2630 (2010)

    Article  Google Scholar 

  41. Khmag, A., Ramli, A., Al Haddad, S.A.R., Hashim, S.J.: Denoising of natural image based on non-linear threshold filtering using discrete wavelet transformation. Int. Rev. Comput. Softw. (IRECOS) 9(8), 1348–1357 (2014)

  42. Atkins, D., Neshatian, K., Zhang, M.: A domain independent genetic programming approach to automatic feature extraction for image classification. In: Evolutionary computation (CEC), congress on IEEE, pp. 238–245 (2011)

  43. Chen, F., Ma, J.: An empirical identification method of Gaussian blur parameter for image deblurring. IEEE Trans. Image Process. 57(7), 2467–2478 (2009)

    Article  MathSciNet  Google Scholar 

  44. Burger, H.C., Schuler, C.J., Harmeling, S.: Image denoising: can plain neural networks compete with BM3D. In: IEEE conference on computer vision and pattern recognition, pp 2392–2399 (2012)

  45. Everingham, M., Van Gool, L., Williams, CKI., Winn, J., Zisserman, A.: Pascal visual object classes challenge results. http://www.pascal-network.org (2005)

  46. Poli, R., Langdon, W.P., McPhee, N.F., Koza, J.R.: A Field Guide to Genetic Programming. Lulu Enterprises UK Ltd, London (2008)

    Google Scholar 

  47. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  48. Rajwade, A., Rangarajan, A., Banerjee, A.: Image denoising using the higher order singular value decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 35(4), 849–862 (2013)

    Article  Google Scholar 

  49. Zhang, M., Gunturk, B.K.: Multiresolution bilateral filtering for image denoising. IEEE Trans. Image Process. 17(12), 2324–2333 (2008)

  50. Hwang, H., Haddad, R.: Adaptive median filters: new algorithms and results. IEEE Trans. Image Process. 4(4), 499–502 (1995)

    Article  Google Scholar 

  51. Xiong, B., Yin, Z.: A universal denoising framework with a new impulse detector and nonlocal means. IEEE Trans. Image Process. 21(4), 1663–1675 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their constructive comments in improving the quality of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Asem Khmag.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khmag, A., Ramli, A.R., Al-haddad, S.A.R. et al. Denoising of natural images through robust wavelet thresholding and genetic programming. Vis Comput 33, 1141–1154 (2017). https://doi.org/10.1007/s00371-016-1273-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-016-1273-5

Keywords

Navigation