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Color monogenic wavelet transform for multichannel image denoising

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Abstract

This paper proposes an effective color image denoising algorithm using the combination color monogenic wavelet transform (CMWT) with a trivariate shrinkage filter. The CMWT coefficients are one order of magnitude with three phases: two phases encode the local color information while the third contains geometric information relating to texture within the color image. In the CMWT domain, a trivariate Gaussian distribution is applied to capture statistical dependencies between the CMWT coefficients, and then a trivariate shrinkage filter is derived using a maximum a posteriori estimator. The performance of the proposed algorithm is experimentally verified using a variety of color test images with a range of noise levels in terms of PSNR and visual quality. The experimental results demonstrate that the proposed algorithm is equal to or better than current state-of-the-art algorithms in both visual and quantitative performance.

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References

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

    Article  Google Scholar 

  • Awate, S. P., & Whitaker, R. T. (2006). Unsupervised information-theoretic adaptive image filteringfor image restoration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 28(3), 364–376.

    Article  Google Scholar 

  • Baudes, A. C., & Morel, J. M. (2005). A review of image denoising methods, with a new one. Multiscale Model Simulation, 4(2), 490–530.

    Article  MathSciNet  Google Scholar 

  • Chatterjee, P., & Milanfar, P. (2009). Clustering-based denoising with locally learned dictionaries. IEEE Transactions on Image Processing, 18(7), 1438–1451.

    Article  MathSciNet  Google Scholar 

  • Chatterjee, P., & Milanfar, P. (2012). Patch-based near-optimal image denoising. IEEE Transactions on Image Processing, 21(4), 1635–1649.

    Article  MathSciNet  Google Scholar 

  • Crespo, N., & Simoes, N. (2012). On the measurement of a multidimensional concept of structural similarity. Economics Letters, 116(1), 115–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Cunha, A. L., Zhou, J. P., & Do, M. N. (2006). The nonsubsampled contourlet transform: Theory, design, and applications. IEEE Transactions on Image Processing, 15(10), 3089–3101.

    Article  Google Scholar 

  • Dabov, K., Foi, A., Katkovik, V., & Egiazarian, K. O. (2007). Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Transactions on Image Processing, 16(8), 2080–2095.

    Article  MathSciNet  Google Scholar 

  • Demarcq, G., Mascarilla, L., Berthier, M., & Courtellemont, P. (2011). The color monogenic signal: Application to color edge detection and color optical flow. Mathematical Imaging and Vision, 40(3), 269–284.

    Article  MathSciNet  MATH  Google Scholar 

  • Dong, G. G., Wang, N., & Kuang, G. Y. (2014). Sparse representation of monogenic signal: With application to target recognition in SAR images. IEEE Signal Processing Letters, 21(8), 952–956.

    Article  Google Scholar 

  • Donoho, D. L. (1995). Denoising by soft-thresholding. IEEE Transactions on Information Theory, 41(3), 613–627.

    Article  MathSciNet  MATH  Google Scholar 

  • Do, M. N., & Vetterli, M. (2006). The contourlet transform: An efficient directional multiresolution image representation. IEEE Transaction on Image Processing, 14(12), 2091–2106.

    Article  Google Scholar 

  • Duits, R., Felsberg, M., Florack, L., & Platel, B. (2003). \(\alpha \)-scale spaces on a bounded domain. In proceedings Scale-Space, LNCS 2695, Berlin, Heidelberg: Springer-Verlag, 2003, (pp. 494-510).

  • Easleya, G., Labate, D., & Lim, W. Q. (2008). Sparse directional image representations using the discrete shearlet transform. Applied and Computational Harmonic Analysis, 25(1), 25–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Elad, M., & Aharon, M. (2006). Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing, 15(12), 3736–3745.

    Article  MathSciNet  Google Scholar 

  • Felsberg, M., & Sommer, G. (2001). The monogenic signal. IEEE Transactions on Signal Processing, 49(12), 3136–3144.

    Article  MathSciNet  Google Scholar 

  • Held, S., Storath, M., Massopust, P., & Forster, B. (2010). Steerable wavelet frames based on the Riesz transform. IEEE Transactions on Image Processing, 19(3), 653–667.

    Article  MathSciNet  Google Scholar 

  • Lim, W. Q. (2010). The discrete shearlet transform: A new directional transform and compactly supported shearlet frames. IEEE Transactions on Image Processing, 19(5), 1166–1180.

    Article  MathSciNet  Google Scholar 

  • Liu, C., Szeliski, R., Kang, S. B., Zitnick, C. L., & Freeman, W. T. (2008). Automatic estimation and removal of noise from a single image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 30(2), 299–314.

    Article  Google Scholar 

  • Muresan, D. D., & Parks, T. W. (2003). Adaptive principle components and image denoising. IEEE Conference on Image Processing, Bacelona, Spain, September, 2003 (pp. 101–104).

  • Naveed, R., & Mandic, D. P. (2010). Empirical mode decomposition for trivariate signals. IEEE Transactions on Signal Processing, 58(3), 1059–1068.

    Article  MathSciNet  Google Scholar 

  • Olhede, S. C., & Metikas, G. (2009). The monogenic wavelet transform. IEEE Transactions on Signal Processing, 57(9), 3426–3441.

    Article  MathSciNet  Google Scholar 

  • Olhede, S. C., Ramirez, D., & Schreier, P. J. (2014). Detecting directionality in random fields using the monogenic signal. IEEE Transactions on Information Theory, 60(10), 6491–6510.

    Article  MathSciNet  MATH  Google Scholar 

  • Pennec, E. L., & Mallat, S. (2005). Sparse geometric image representations with bandelets. IEEE Transactions on Image Processing, 14(4), 423–438.

    Article  MathSciNet  Google Scholar 

  • Portilla, J., Strela, V., Waiwright, M., & Simoncelli, E. (2003). Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Transactions on Image Processing, 12(11), 1338–1351.

    Article  MathSciNet  MATH  Google Scholar 

  • Selesnick, I. W., Baraniuk, R. G., & Kingsbury, N. (2005). The dual-tree complex wavelet transform-A coherent framework for multiscale signal and image processing. IEEE Transactions on Signal Processing, 22(6), 123–151.

    Article  Google Scholar 

  • Soulard, R., Carre, P., & Maloigne, C. F. (2013). Vector extension of monogenic wavelets for geometric representation of color images. IEEE Transactions on Image Processing, 22(3), 1070–1083.

    Article  MathSciNet  Google Scholar 

  • Unser, M., Van, D., & Ville, D. (2008). The pairing of a wavelet basis with a mildly redundant analysis via subband regressioin. IEEE Transactions on Image Processing, 17(11), 2040–2052.

    Article  MathSciNet  Google Scholar 

  • User, M., Sage, D., & Ville, D. (2009). Multiresolution monogenic signal analysis using the Riesz–Laplace wavelet transform. IEEE Transactions on Image Processing, 18(11), 2402–2418.

    Article  MathSciNet  Google Scholar 

  • Van, D., Ville, D., Blu, T., & Unser, M. (2005). Isotropic polyharmonic b-splines: Scaling functions and wavelets. IEEE Transactions on Image Processing, 14(11), 1798–1813.

    Article  MathSciNet  Google Scholar 

  • Veilsavljevic, V., Beferull-Lozano, B., Vetterli, M., & Dragotti, P. L. (2006). Directionlets: Anisotropic multidirectional representation with separable filtering. IEEE Transactions on Image Processing, 15(7), 1916–1933.

    Article  Google Scholar 

  • Wang, Y. J. (2001). Modeling of random variation of three-phase voltage unbalance in electric distribution systems using the trivariate Gaussian distribution. IEE Proceedings-Generation, Transmission and Distribution, 148(4), 279–284.

    Article  Google Scholar 

  • Yan, S., Yang, X. Y., & Guo, Y. H. (2014). Translation invariant directional framelet transform combined with Gabor filters for image denoising. IEEE Transactions on Image Processing, 23(1), 44–55.

    Article  MathSciNet  Google Scholar 

  • Yuksel, M. E., & Basturk, A. (2012). Application of type-2 fuzzy logic filtering to reduce noise in color images. IEEE Transactions on Computational Intelligence Magazine, 7(3), 25–35.

    Article  Google Scholar 

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

  • Zhang, L., Dong, W., Zhang, D., & Shi, G. (2010). Two-stage image denoising by principle component analysis with local pixel grouping. Pattern Recognition, 43(4), 1531–1549.

    Article  MATH  Google Scholar 

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Acknowledgments

This work is partially supported by National Natural Science Foundation of China under Grant Nos.(61563037, 61402218); Jiangxi Provincial Natural Science Foundation of China under Grant No. (20151BAB207031); Department of Education Science and Technology of Jiangxi Province under Grant No. (GJJ150755).

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Authors and Affiliations

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

    Shan Gai, Yong Zhang, Cihui Yang, Lei Wang & Jiehua Zhou

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  1. Shan Gai
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  2. Yong Zhang
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  3. Cihui Yang
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  4. Lei Wang
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  5. Jiehua Zhou
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Correspondence to Shan Gai.

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Gai, S., Zhang, Y., Yang, C. et al. Color monogenic wavelet transform for multichannel image denoising. Multidim Syst Sign Process 28, 1463–1480 (2017). https://doi.org/10.1007/s11045-016-0426-z

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  • DOI: https://doi.org/10.1007/s11045-016-0426-z

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