Skip to main content
SpringerLink
Log in

Texture preserving denoising method combining total variation and wavelet shrinkage

  • Published:
Wuhan University Journal of Natural Sciences

Abstract

In this paper, we propose a new image denoising method that combines total variation (TV) method and wavelet shrinkage. In our method, a noisy image is decomposed into subbands of LL, LH, HL, and HH in wavelet domain. LL subband contains the low frequency coefficients along with less noise, which can be easily eliminated using TV-based method. More edges and other detailed information like textures are contained in the other three subbands, and we propose a shrinkage method based on the local variance to extract them from high frequency noise. Experimental results show that this method retains the edges and textures very well while removing noise.

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

Similar content being viewed by others

References

  1. Aujol J F, Chambolle A. Dual norms and image decomposition models[J]. International Journal on Computer Vision, 2005, 63(1): 85–104.

    Article  MathSciNet  Google Scholar 

  2. Rudin L, Osher S, Fatemi E. nonlinear total variation based noise removal algorithms[J]. Physica D, 1992, 60: 259–268.

    Article  MATH  Google Scholar 

  3. Chambolle A. An algorithm for total variation minimization and applications[J]. Journal of Mathematical Imaging and Vision, 2004, 20(1–2): 89–97.

    MathSciNet  Google Scholar 

  4. Osher S, Sole A, Vese L. Image decomposition and restoration using total variation minimization and the H −1 norm[J]. SIAM Journal on Multiscale Modeling and Simulation, 2003, 1(3): 349–370.

    Article  MATH  MathSciNet  Google Scholar 

  5. Vese L, Osher S. Modeling textures with total variation minimization and oscillating patterns in image processing[J]. Journal of Scientific Computing, 2003, 19: 553–572.

    Article  MATH  MathSciNet  Google Scholar 

  6. Gilboa G, Sochen N, Zeevi Y Y. Texture preserving variational denoising using an adaptive fidelity term[J]. IEEE Transactions on Image Processing, 2006, 15(8): 2281–2289.

    Article  Google Scholar 

  7. Meyer Y. Oscillating patterns in image processing and nonlinear evolution equations[C]//The Fifteenth Dean Jacque Lines B, Lewis Memorial Lectures. Rhode Island: American Mathematical Society Press, 2002.

    Google Scholar 

  8. Donoho D L, Johnstone I M. Denoising by soft thresholding[J]. IEEE Transactions on Information Theory, 1995, 41: 613–627.

    Article  MATH  Google Scholar 

  9. Donoho D L, Johnstone I M. Ideal spatial adaptation by wavelet shrinkage[J]. Biomerika, 1994, 81: 425–455.

    Article  MATH  MathSciNet  Google Scholar 

  10. Donoho D L, Johnstone I M. Adapting to unknown smoothness via wavelet shrinkage[J]. J Amer Statist Assoc, 1995, 90: 1200–1224.

    Article  MATH  MathSciNet  Google Scholar 

  11. Chang S, Yu B, Vetterli M. Adaptive wavelet thresholding for image denoising and compression[J]. IEEE Transactions on Image Processing, 2000, 9: 1532–1546.

    Article  MATH  MathSciNet  Google Scholar 

  12. Chambolle A, Devore R, Lee N, et al. Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage[J]. IEEE Transactions on Image Processing, 1998, 7(3): 319–335.

    Article  MATH  MathSciNet  Google Scholar 

  13. Daubechies I. The wavelet transform, time-frequency localization and signal analysis[J]. IEEE Transactions on Information Theory, 1990, 36: 961–1005.

    Article  MATH  MathSciNet  Google Scholar 

  14. Daubechies I, Teschke G. Variational image restoration by means of wavelets: simultaneous decomposition, deblurring, and denoising[J]. Applied and Computational Harmonic Analysis, 2005, 19: 1–16.

    Article  MATH  MathSciNet  Google Scholar 

  15. Durand S, Froment J. Reconstruction of wavelet coefficients using total variation minimization[J]. SIAM Journal on Scientific Computing, 2003, 24: 1754–1767.

    Article  MATH  MathSciNet  Google Scholar 

  16. Chan T F, Zhou H M. Total variation improved wavelet thresholding in image compression[C]//Proceeding of the Seventh International Conferrence on Image Processing. Washington D C: IEEE Press, 2000: 391–394.

    Google Scholar 

  17. Coifman R R, Sowa A. Combing the calculus of variations and wavelets for image enhancement[J]. Appl Compt Harmon Ana, 2000, 9:1–18.

    Article  MATH  MathSciNet  Google Scholar 

  18. Steidl G, Weickert J, Brox T, et al. On the equivalence of soft wavelet shrinkage, total variation diffusion, total variation regularization, and sides[J]. SIAM Journal on Numerical Analysis, 2004, 42: 686–713.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China

    Tao Zhang & Qibin Fan

Authors
  1. Tao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qibin Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qibin Fan.

Additional information

Foundation item: Supported by the National High Technology Research and Development Program of China (863 Program) (2008AA12Z201)

Biography: ZHANG Tao, male, Ph.D. candidate, research direction: wavelet analysis.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhang, T., Fan, Q. Texture preserving denoising method combining total variation and wavelet shrinkage. Wuhan Univ. J. Nat. Sci. 15, 31–35 (2010). https://doi.org/10.1007/s11859-010-0107-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-010-0107-y

Key words

CLC number

Search

Navigation