Skip to main content
SpringerLink
Log in

Multiresolution Monogenic Wavelet Transform Combined with Bivariate Shrinkage Functions for Color Image Denoising

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

Abstract

This paper studies and gives a new algorithm for vector-valued signal processing based on multiresolution monogenic wavelet transform (MMWT). The Riesz transform is employed in the synthesis part of the MMWT. The MMWT coefficients can provide comprehensive analysis of amplitude, phase and orientation for image processing. To demonstrate the properties of MMWT, new color image denoising algorithm is proposed by using MMWT and bivariate shrinkage function. The performance of the proposed algorithm is experimentally verified by using different test color images and noise levels in terms of peak signal-to-noise ratio value and visual quality. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that the proposed algorithm can obtain better denoising performance in both visual and quantitative performances. Computation time of the proposed method is analyzed and compared with existing approaches.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. M. Alessandrini, O. Bernard, A. Basarab, H. Liebott, Multiscale optical flow computation from the monogenic signal. IRBM 34(1), 33–37 (2013)

    Article  Google Scholar 

  2. C. Amiot, C. Girard, J. Chanussot, J. Pescatore, M. Desvignes, Curvelet based contrast enhancement in fluoroscopic sequences. IEEE Trans. Med. Imaging 34(1), 137–147 (2015)

    Article  Google Scholar 

  3. S. Azadeh, B.P. Hobbs, L. Ma, D.A. Nielsen, F.G. Moeller, B. Veerabhadran, Integrative Bayesian analysis of neuroimaging-genetic data with application to cocaine dependence. NeruoImage 125(15), 813–824 (2016)

    Article  Google Scholar 

  4. G. Chaitra, D.K. Tapas, S. Enkemann, S. Eschrich, Removal of hybridization and scanning noise from microarrays. IEEE Trans. Nanobiosci. 8(3), 210–218 (2009)

    Article  Google Scholar 

  5. G.Y. Chen, S. Qian, Denoising of hyperspectral imagery using principal component analysis and wavelet shrinkage. IEEE Trans. Geosci. Remote Sens. 49(3), 973–980 (2011)

    Article  Google Scholar 

  6. A.L. Cunha, J.P. Zhou, M.N. Do, The nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans. Image Process. 15(10), 3089–3101 (2006)

    Article  Google Scholar 

  7. G. Demarcq, L. Mascarilla, M. Berthier, P. Courtellemont, The color monogenic signal: application to color edge detection and color optical flow. Math. Imaging Vis. 40(3), 269–284 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. M.N. Do, M. Vetterli, The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14(12), 2091–2106 (2009)

    Article  Google Scholar 

  9. G.G. Dong, N. Wang, G.Y. Kuang, Sparse representation of monogenic signal: with application to target recognition in SAR images. IEEE Signal Process. Lett. 21(8), 952–956 (2014)

    Article  Google Scholar 

  10. G. Easleya, D. Labate, W.Q. Lim, Sparse directional image representations using the discrete shearlet transform. Appl. Comput. Harmon. A. 25(1), 25–46 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. T.A. Ell, S.J. Sangwine, Hypercomplex fourier transforms of color images. IEEE Trans. Image Process. 16(1), 22–35 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Felsberg, G. Sommer, The monogenic signal. IEEE Trans. Signal Process. 49(12), 3136–3144 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  13. D. Garbor, Theory of communication. J. Inst. Electr. Eng. 93(26), 429–441 (1946)

    Google Scholar 

  14. H. Hatsuda, Robust smoothing of quantitative genomic data using second-generation wavelets and bivariate shrinkage. IEEE Trans. Biomed. Eng. 59(8), 2099–2102 (2012)

    Article  Google Scholar 

  15. S. Held, M. Storath, P. Massopust, B. Forster, Steerable wavelet frames based on the riesz transform. IEEE Trans. Image Process. 19(3), 653–667 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  16. P.R. Hill, N. Anantrasirichai, A. Achim, M.E. Ai-Mualla, D.R. Bull, Undecimated dual-tree complex wavelet transforms. Signal Process. Image Commun. 35(6), 61–70 (2015)

    Article  Google Scholar 

  17. W.Q. Lim, The discrete shearlet transform: a new directional transform and compactly supported shearlet frames. IEEE Trans. Image Process. 19(5), 1166–1180 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. B.R. Lim, H.S. Lee, R.H. Park, S.J. Yang, A wavelet packet-based noise reduction algorithm of NTSC images using CVBS characteristics. IEEE Trans. Consum. Electron. 55(4), 2407–2415 (2009)

    Article  Google Scholar 

  19. A. Loza, D.R. Bull, P.R. Hill, A.M. Achim, Automatic contrast enhancement of low-light images based on local statistics of wavelet coefficients. Digit. Signal Process. 23(6), 1856–1866 (2013)

    Article  Google Scholar 

  20. R. Minhas, A.A. Mohammed, Q.M. Jonathan, Shape from focus using fast discrete curvelet transform. Pattern Recognit. 44(4), 839–853 (2011)

    Article  Google Scholar 

  21. S.C. Olhede, G. Metikas, The monogenic wavelet transform. IEEE Trans. Signal Process. 57(9), 3426–3441 (2009)

    Article  MathSciNet  Google Scholar 

  22. S.C. Olhede, D. Ramirez, P.J. Schreier, Detecting directionality in random fields using the monogenic signal. IEEE Trans. Inf. Theory. 60(10), 6491–6510 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  23. H. Rabbani, N. Reza, G. Saeed, Wavelet-domain medical image denoising using bivariate Laplacian mixture model. IEEE Trans. Biomed. Eng. 56(12), 2826–2837 (2009)

    Article  Google Scholar 

  24. I.W. Selesnick, R.G. Baraniuk, N. Kingsbury, The dual-tree complex wavelet transform-a coherent framework for multiscale signal and image processing. IEEE Trans. Signal Process. 22(6), 123–151 (2005)

    Article  Google Scholar 

  25. L. Sendur, I.W. Selesnick, Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Signal Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  26. L. Sendur, V. Maxim, B. Whitcher, E. Bullmore, Multiple hypothesis mapping of functional MRI data in orthogonal and complex wavelet domains. IEEE Trans. Signal Process. 53(9), 3413–3426 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  27. R. Sethunadh, T. Thomas, Spatially adaptive image denoising using inter-scale dependence in directionlet domain. IET Image Process. 9(2), 142–152 (2015)

    Article  Google Scholar 

  28. R. Soulard, P. Carre, C.F. Maloigne, Vector extension of monogenic wavelets for geometric representation of color images. IEEE Trans. Image Process. 22(3), 1070–1083 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Soulard, P. Carre, Elliptical monogenic wavelets for the analysis and processing of color images. IEEE Trans. Signal Process. 64(6), 1535–1549 (2016)

    Article  MathSciNet  Google Scholar 

  30. M. Unser, D. Sage, D. Ville, Multiresolution monogenic signal analysis using the Riesz–Laplace wavelet transform. IEEE Trans. Image Process. 18(11), 2402–2418 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  31. M. Unser, D. Van, D. Ville, Wavelet steerability and the higher-order Riesz transform. IEEE Trans. Image Process. 19(3), 636–652 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. V. Veilsavljevic, B. Beferull-Lozano, M. Vetterli, P.L. Dragotti, Directionlets: anisotropic multidirectional representation with separable filtering. IEEE Trans. Image Process. 15(7), 1916–1933 (2006)

    Article  Google Scholar 

  33. L. Zhang, D. Zhang, Z.H. Guo, Monogenic-LBP: a new approach for rotation invariant texture classification, in IEEE International Conference on Image Processing, pp. 2677–2680 (2010)

Download references

Acknowledgements

This work is partially supported by National Natural Science Foundation of China Under Grant No. (61563037); Natural Science Foundation of Jiangxi Province Under Grant No. (20171BBB202018); and Department of Education Science and Technology of Jiangxi Province Under Grant No. (GJJ150755).

Author information

Authors and Affiliations

  1. The School of Information Engineering, Nanchang Hangkong University, Nanchang, Jiangxi, China

    Shan Gai

Authors
  1. Shan Gai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shan Gai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gai, S. Multiresolution Monogenic Wavelet Transform Combined with Bivariate Shrinkage Functions for Color Image Denoising. Circuits Syst Signal Process 37, 1162–1176 (2018). https://doi.org/10.1007/s00034-017-0597-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-017-0597-3

Keywords

Search

Navigation