[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Energy-based adaptive orthogonal FRIT and its application in image denoising

  • Published:
Science in China Series F: Information Sciences Aims and scope Submit manuscript

Abstract

Efficient representation of linear singularities is discussed in this paper. We analyzed the relationship between the “wrap around” effect and the distribution of FRAT (Finite Radon Transform) coefficients first, and then based on study of some properties of the columnwisely FRAT reconstruction procedure, we proposed an energy-based adaptive orthogonal FRIT scheme (EFRIT). Experiments using nonlinear approximation show its superiority in energy concentration over both Discrete Wavelet Transform (DWT) and Finite Ridgelet Transform (FRIT). Furthermore, we have modeled the denoising problem and proposed a novel threshold selecting method. Experiments carried out on images containing strong linear singularities and texture components with varying levels of addictive white Gaussian noise show that our method achieves prominent improvement in terms of both SNR and visual quality as compared with that of DWT and FRIT.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Candes E J, Donoho D L. Ridgelets: a key to higher-dimensional intermittency. Philos Trans R Soc A-Math Phys Eng Sci, 1999, 357(1760): 2495–2509

    Article  MATH  MathSciNet  Google Scholar 

  2. Starck J-L, Candes E J, Donoho D L. The curvelet transform for image denoising. IEEE Trans Image Process, 2002, 11(6): 670–684

    Article  MathSciNet  Google Scholar 

  3. Donoho D L. Ridge functions and orthonormal ridgelets. J Approx Theory, 2001, 111: 143–179

    Article  MATH  MathSciNet  Google Scholar 

  4. Donoho D L, Flesia A G. Digital Ridgelet Transform Based on True Ridge Functions. 2001, http://www-stat.stanford.edu/:_donoho/reports.html

  5. Do M N, Vetterli M. The finite ridgelet transform for image representation. IEEE Trans Image Process, 2003, 12(1): 16–28

    Article  MathSciNet  Google Scholar 

  6. Matus F, Flusser J. Image representation via a finite Radon transform. IEEE Trans Pattern Anal Mach Intell, 1993, 15(10): 996–1006

    Article  Google Scholar 

  7. Granai L, Moschetti F, Vandergheynst P. Ridgelet transform applied to motion compensated images. In: Proceedings of 2003 International Conference on Multimedia and Expo (ICME’03), 2003, 1: 561–564

    Google Scholar 

  8. Zhang P, Ni L. The curvelet transform based on finite ridgelet transform for image denoising. In: Proceedings of Seventh International Conference on Signal Processing (ICSP’04), 2004, 2: 978–981

    Article  Google Scholar 

  9. Campisi P, Kundur D, Neri A. Robust digital watermarking in the Ridgelet domain. IEEE Signal Process Lett, 2004, 11(10): 826–830

    Article  Google Scholar 

  10. Hou B, Jiao L C, Liu F. Image denoising based on ridgelet. In: Proceedings of Sixth International Conference on Signal Processing (ICSP’04), 2002, 1: 780–783

    Google Scholar 

  11. Liu Y X, Peng Y H, Zhou X H. Texture classification using finite ridgelet transform and support vector machines. In: Proceedings of Ninth Pacific Rim International Conference on Artificial Intelligence (PRICAI’06), 2006, 4099: 1042–1046

    Google Scholar 

  12. Nezamoddini-Kachouie N, Fieguth P, Jernigan E. BayesShrink Ridgelets for Image Denoising. In: Proceedings of International Conference on Image Analysis and Recognition (ICIAR’04), 2004, PT1: 163–170

    Google Scholar 

  13. Xiao X K, Li S F. Edge-preserving image denoising method using Curvelet transform. J Commun (in Chinese), 2004, 25(2): 9–15

    Google Scholar 

  14. Brodatz, Textures: http://www.ux.uis.no/:_tranden/brodatz.html

  15. FRAT Toolbox: http://www.ifp.uiuc.edu/:_minhdo/software/frit_toolbox.tar.gz

  16. Donoho D L, Johnstone I M. Ideal spatial adaptation via wavelet shrinkage. Biometrika, 1994, 81: 425–455

    Article  MATH  MathSciNet  Google Scholar 

  17. Chang S G, Yu B, Vetterli M. Adaptive wavelet thresholding for image denoising and compression. IEEE Trans Image Process, 2000, 9(9): 1532–1546

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Shandong University, Jinan, 250100, China

    Liu YunXia, Peng YuHua & Qu HuaiJing

  2. Shandong Tumor Hospital, Jinan, 250117, China

    Yin Yong

Authors
  1. Liu YunXia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peng YuHua
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qu HuaiJing
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yin Yong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liu YunXia.

Additional information

Supported by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, the Ministry of Education (Grant No. 2004.176.4), and the Natural Science Foundation of Shandong Province (Grant Nos. Z2004G01 and 2004ZRC03016)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Y., Peng, Y., Qu, H. et al. Energy-based adaptive orthogonal FRIT and its application in image denoising. SCI CHINA SER F 50, 212–226 (2007). https://doi.org/10.1007/s11432-007-0013-x

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11432-007-0013-x

Keywords

Search

Navigation