Soft Computing

, Volume 22, Issue 2, pp 635–644 | Cite as

Multichannel image denoising using color monogenic curvelet transform

  • Shan Gai
Methodologies and Application


Color monogenic curvelet transform (CMCT) is a new multi-scale analysis tool for geometric image features. CMCT has useful properties that it behaves at the fine scales like curvelet transform and at the coarse scales like the color monogenic wavelet transform. CMCT has one magnitude and three phases which encode geometric information of color images. In order to demonstrate the properties of CMCT, new color image denoising algorithm is proposed based on CMCT and total variation. The experimental results demonstrate that the proposed algorithm is at par with or exceeds current state-of-the-art algorithms in both visual and quantitative performance.


Curvelet transform Analytic signal Color monogenic wavelet transform Total variation Color image denoising 



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. (20151BAB207031); Department of Education Science and Technology of Jiangxi Province under Grant No. (GJJ150755).

Compliance with ethical standards

Conflict of interest

The author Shan Gai in this paper declares no conflict of interest.


  1. Alessandrini M, Bernard O, Basarab A, Liebott H (2013) Multiscale optical flow computation from the monogenic signal. IRBM 34(1):33–37CrossRefGoogle Scholar
  2. Amiot C, Girard C, Chanussot J, Pescatore J, Desvignes M (2015) Curvelet based contrast enhancement in fluoroscopic sequences. IEEE Trans Med Imaging 34(1):137–147CrossRefGoogle Scholar
  3. Candes EJ, Donoho DL (2005) Continuous curvelet transform: I. Resolution of the wavefront set. Appl Comput Harmonic Anal 19(8):162–197MathSciNetCrossRefzbMATHGoogle Scholar
  4. Candes EJ, Donoho DL (2005) Continuous curvelet transform: II. Discretization and frames. Appl Comput Harmonic Anal 19(2):198–222MathSciNetCrossRefzbMATHGoogle Scholar
  5. Cunha AL, Zhou JP, Do MN (2006) The Nonsubsampled contourlet transform: theory, design, and applications. IEEE Trans Image Process 15(10):3089–3101CrossRefGoogle Scholar
  6. Demarcq G, Mascarilla L, Berthier M, Courtellemont P (2011) The color monogenic signal: application to color edge detection and color optical flow. Math Imag Vis 40(3):269–284MathSciNetCrossRefzbMATHGoogle Scholar
  7. Dong GG, Wang N, Kuang GY (2014) Sparse representation of monogenic signal: with application to target recognition in sar images. IEEE Signal Process Lett 21(8):952–956CrossRefGoogle Scholar
  8. Do MN, Vetterli M (2006) The contourlet transform:an efficient directional multiresolution image representation. IEEE Trans Image Process 14(12):2091–2106CrossRefGoogle Scholar
  9. Easleya G, Labate D, Lim WQ (2008) Sparse directional image representations using the discrete shearlet transform. Appl Comput Harmonic Anal 25(1):25–46MathSciNetCrossRefzbMATHGoogle Scholar
  10. Held S, Storath M, Massopust P, Forster B (2010) Steerable wavelet frames based on the riesz transform. IEEE Trans Image Process 19(3):653–667MathSciNetCrossRefzbMATHGoogle Scholar
  11. Holt KM (2014) Total nuclear variation and jacobian extensions of total variation for vector fields. IEEE Trans Image Process 23(9):3975–3989MathSciNetCrossRefzbMATHGoogle Scholar
  12. Hughes JM, Rockmore DN, Yang W (2013) Bayesian learning of sparse multiscale image representations. IEEE Trans Image Process 22(12):4972–4983MathSciNetCrossRefzbMATHGoogle Scholar
  13. Kim S (2006) PDE-based image restoration: a hybrid model and color image denoising. IEEE Trans Image Process 15(5):1163–1170CrossRefGoogle Scholar
  14. Kim SJ, Kang W, Lee E, Paik J (2010) Wavelet-domain color image enhancement using filtered directional bases and frequency-adaptive shrinkage. IEEE Trans Consum Electron 56(2):1063–1070CrossRefGoogle Scholar
  15. Lian NX, Zagorodnov V, Tan YP (2005) Color image denoising using wavelets and minimum cut analysis. Signal Process Lett 12(11):741–744CrossRefGoogle Scholar
  16. Lim BR, Lee HS, Park RH, Yang SJ (2009) A wavelet packet-based noise reduction algorithm of NTSC images using CVBS characteristics. IEEE Trans Consum Electron 55(4):2407–2415CrossRefGoogle Scholar
  17. Lim WQ (2010) The discrete shearlet transform: a new directional transform and compactly supported shearlet frames. IEEE Trans Image Process 19(5):1166–1180MathSciNetCrossRefzbMATHGoogle Scholar
  18. Luisier F, Blu T (2008) SURE-LET multichannel image denoising: interscale orthonormal wavelet thresholding. IEEE Trans Image Process 17(4):482–492MathSciNetCrossRefGoogle Scholar
  19. Olhede SC, Ramirez D, Schreier PJ (2014) Detecting directionality in random fields using the monogenic signal. IEEE Trans Inf Theory 60(10):6491–6510MathSciNetCrossRefzbMATHGoogle Scholar
  20. Pennec EL, Mallat S (2005) Sparse geometric image representations with bandelets. IEEE Trans Image Process 14(4):423–438MathSciNetCrossRefGoogle Scholar
  21. Pizurica A, Philips W (2006) Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising. IEEE Trans Image Process 15(3):654–665CrossRefGoogle Scholar
  22. Selesnick IW, Baraniuk RG, Kingsbury N (2005) The dual-tree complex wavelet transform-A coherent framework for multiscale signal and image processing. IEEE Trans Signal Process 22(6):123–151CrossRefGoogle Scholar
  23. Soulard R, Carre P, Maloigne CF (2013) Vector extension of monogenic wavelets for geometric representation of color images. IEEE Trans Image Process 22(3):1070–1083MathSciNetCrossRefzbMATHGoogle Scholar
  24. Veilsavljevic V, Beferull-Lozano B, Vetterli M, Dragotti PL (2006) Directionlets: anisotropic multidirectional representation with separable filtering. IEEE Trans Image Process 15(7):1916–1933CrossRefGoogle Scholar
  25. Wen YW, Ng MK, Huang YM (2008) Efficient total variation minimization methods for color image restoration. IEEE Trans Image Process 17(11):2081–2088MathSciNetCrossRefzbMATHGoogle Scholar
  26. Zhang DG (2012) A new approach and system for attentive mobile learning based on seamless migration. Appl Intell 36(1):75–89CrossRefGoogle Scholar
  27. Zhang DG, Kang XJ (2012a) A novel image denoising method based on spherical coordinates system. EURASIP J Adv Signal Process 110:1–10Google Scholar
  28. Zhang DG, Zhang XD (2012b) Design and implementation of embedded un-interruptible power supply system (EUPSS) for web-based mobile application. Enterp Inform Syst 6(4):473–489CrossRefGoogle Scholar
  29. Zhang DG, Zhu YN (2012c) A new constructing approach for a weighted topology of wireless sensor networks based on local-world theory for the Internet of Things (IOT). Comput Math Appl 64(5):1044–1055CrossRefzbMATHGoogle Scholar
  30. Zhang L, Zhang D, Guo ZH (2010) Monogenic-LBP: A new approach for rotation invariant texture classification. IEEE international conference on image processing, pp 2677–2680Google Scholar
  31. Zhang DG, Li G, Zheng K (2014a) An energy-balanced routing method based on forward-aware factor for Wireless Sensor Network. IEEE Trans Ind Inf 10(1):766–773CrossRefGoogle Scholar
  32. Zhang DG, Wang X, Song XD (2014b) A novel approach to mapped correlation of ID for RFID anti-collision. IEEE Trans Serv Comput 7(4):741–748CrossRefGoogle Scholar
  33. Zhang DG, Song XD, Wang X (2015a) New agent-based proactive migration method and system for big data environment (BDE). Eng Comput 32(8):2443–2466CrossRefGoogle Scholar
  34. Zhang DG, Wang X, Song XD (2015b) New medical image fusion approach with coding based on SCD in wireless sensor network. J Elect Eng Technol 10(6):2384–2392CrossRefGoogle Scholar
  35. Zhang DG, Zheng K, Zhang T (2015c) A novel multicast routing method with minimum transmission for WSN of cloud computing service. Soft Comput 19(7):1817–1827CrossRefGoogle Scholar
  36. Zhang DG, Liang YP (2013) A kind of novel method of service-aware computing for uncertain mobile applications. Math Comput Model 57(3–4):344–356CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Information EngineeringNanchang Hangkong UniversityJiangxi NanchangPeople’s Republic of China

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