Skip to main content
SpringerLink
Log in

A fast computation method for time scale signal denoising

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

This paper presents a novel and fast scheme for signal denoising in the wavelet domain. It exploits the time scale structure of the wavelet coefficients by modeling them as superposition of simple atoms, whose spreading in the time scale plane formally is the solution of a couple of differential equations. In this paper, we will show how the numerical solution of such equations can be avoided leading to a speed up of the scale linking computation. This result is achieved through a suitable projection space of the wavelet local extrema, requiring just least squares and filtering operations. Intensive experimental results show the competitive performances of the proposed approach in terms of signal to noise ratio (SNR), visual quality and computing time.

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. Balster, E.J., Zheng, Y.F., Ewing, R.L.: Feature-based wavelet shrinkage algorithm for image denoising. IEEE Trans. Image Process. vol. 14, No. 12 (2005)

  2. Bruni, V., Vitulano, D.: Wavelet based signal denoising via simple singularities approximation. Signal Processing, vol. 86, pp. 859–876. Elsevier Science, Amsterdam (2006)

  3. Bruni, V., Piccoli, B., Vitulano, D.: Scale space atoms for signals and image de-noising. In: IAC Report (2006)

  4. Chang S.G., Bin Yu, Vetterli M.: Spatially adaptive thresholding with context modeling for image denoising. IEEE Trans. Image Process. 9(9), 1522–1530 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Choi, H., Baraniuk, R.: Analysis of wavelet—domain wiener filters. In: Proceedings of the IEEE—SP International Symposium on Time-frequency and Time-scale Analysis, October (1998)

  6. Crouse M.S., Nowak R.D., Baraniuk R.G.: Wavelet-based statistical signal processing using hidden Markov models. IEEE Trans. Signal Process. 46(4), 886–902 (1998)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  8. Donoho D.L.: Denoising by soft thresholding. IEEE Trans. Inform. Theory 41(3), 613–627 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  9. Dragotti, P.L., Vetterli, M.: Footprints and edgeprints for image denoising and compression. In: Proceedings of IEEE International Conference on Image Processing (ICIP), Thessaloniki, Greece, October (2001)

  10. Dragotti P.L., Vetterli M.: Wavelet footprints: theory, algorithms and applications. IEEE Trans. Signal Process. 51(5), 1306–1323 (2003)

    Article  MathSciNet  Google Scholar 

  11. Fan G., Xia X.: Image denoising using a local contextual hidden Markov model in the wavelet domain. IEEE Signal Process. Lett. 8(5), 125–128 (2001)

    Article  MathSciNet  Google Scholar 

  12. Gilboa G., Sochen N., Zeevi Y.Y.: Image enhancement and denoising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020–1036 (2004)

    Article  Google Scholar 

  13. Kazubek M.: Wavelet domain image denoising by thresholding and wiener filtering. IEEE Signal Process. Lett. 10(11), 324–326 (2003)

    Article  Google Scholar 

  14. Kervrann, C., Boulanger, J.: Unsupervised patch-based image regularization and representation. In: Proceedings of European Conf. Comp. Vision (ECCV’06), Graz, Austria, May (2006)

  15. Koenderink J.: The structure of images. Biol. Cybern. 50, 363–370 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  16. Jaffard, S., Meyer, Y., Ryan, R.D.: Wavelets: Tools for Science and Technology. SIAM, Philadelphia (2001)

  17. Lin, X., Orchard, M.T.: Spatially adaptive image denoising under overcomplete expansion. In: Proceedings of IEEE International Conference on Image Processing, September (2000), pp. 300–303

  18. Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Trans. Inform. Theory, vol. 38, No. 2, March (1992)

  19. Mallat S.: A Wavelet Tour of Signal Processing. Academic Press, New York (1998)

    MATH  Google Scholar 

  20. Mallat S., Zhong S.: Characterization of signals from multiscale edges. IEEE Trans. Pattern Anal. Mach. Intell. 14, 710–732 (1992)

    Article  Google Scholar 

  21. Mihcak M.K., Kozintsev I., Ramchandran K., Moulin P.: Low-complexity image denoising based on statistical modeling of wavelet coefficients. IEEE Signal Process. Lett. 6(12), 300–303 (1999)

    Article  Google Scholar 

  22. Perona P., Malik J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12, 629–639 (1990)

    Article  Google Scholar 

  23. Petrovic, A., Escoda, O.D., Vandergheynst, P.: Multiresolution segmentation of natural images: from linear to nonlinear scale-space representations. IEEE Trans. Image Process., vol. 13, No. 8, August (2004)

  24. Pizurica, A., Philips, W., Lemanhieu, I., Acheroy, M.: A joint inter- and intrascale statistical model for bayesian wavelet based image denoising. IEEE Trans. Image Process., vol. 11, No. 5, May 2002

  25. Portilla J., Strela V., Wainwright M., Simoncelli E.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Trans. Image Process. 12(11), 1338–1351 (2003)

    Article  MathSciNet  Google Scholar 

  26. Shih A.C., Liao H.M., Lu C.: A new iterated two-band diffusion equation: theory and its application. IEEE Trans. Image Process. 12(4), 466–476 (2003)

    Article  MathSciNet  Google Scholar 

  27. Rosenfeld, A., Thurston, M.: Edge and curve detection for visual scene analysis. IEEE Transactions on Comput., vol. C-20, May 1971, pp. 562–569

  28. Sendur, L., Selesnick, I.W.: Bivariate shrinkage with local variance estimation. IEEE Signal Process. Lett., vol. 9, No. 12, December (2002)

  29. Shui P.L.: Image denosing algorithm via doubly local wiener filtering with directional windows in wavelet domain. IEEE Signal Process. Lett. 12(10), 681–684 (2005)

    Article  Google Scholar 

  30. Teboul S., Blanc-Feraud L., Aubert G., Barlaud M.: Variational approach for edge-preserving regularization using coupled PDE’s. IEEE Trans. Image Process. 7(3), 387–397 (1998)

    Article  Google Scholar 

  31. Mrazek P., Weickert J., Steidl G.: Diffusion-inspired shrinkage functions and stability results for wavelet denoising. Int. J. Comput. Vis. 64(2/3), 171–186 (2005)

    Article  Google Scholar 

  32. Witkin, A.: Scale-space filtering. In: Proceedings of the International Joint Conf. Artificial Intelligence, Karlsruhe, West Germany, pp. 1019–1021 (1983)

  33. Zhang, H., Nosratinia, A., Wells, R.O.: Image denoising via wavelet-domain spatially adaptive FIR wiener filtering. In: Proceedings of IEEE International Conf. on Acoustic Speech and Signal Processing 2000, vol. 5, Istanbul, Turkey, June 2000, pp. 2179–2182

  34. Voloshynovskiy, S., Koval, O., Pun, T.: Image denoising based on the edge-process model. Signal Processing, Elsevier Science, Amsterdam (2006)

  35. Wei J.: Lebesgue Anisotropic Image Denoising. Wiley Periodicals Inc., London (2005)

    Google Scholar 

  36. Pizurica, A., Philips, W.: Estimating the probability of the presence of a signal of interest in multiresolution single and multiband image denoising. IEEE Trans. Image Process. (2007)

  37. Charest, M.R., Elad, M., Milanfar, P.: A general iterative regularization framework for image denosing. In: Proceedings of the 40th Conference on Information Sciences and Systems, Princeton, NJ, March (2006)

  38. Luisier, F., Blu, T., Unser, M.: A new SURE approach to image denoising: interscale orthonormal wavelet thresholding. IEEE Trans. Image Process., vol. 16, No. 3, March (2007)

  39. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms with a new one. Multiscale Model. Simul., vol. 4, No. 2, Society for industrial and Applied Mathematics, pp. 490–530 (2005)

  40. Elad, M., Aharon, M.: Image denoising via learned dictionaries and sparse representation. In: Proceedings of IEEE CVPR’06 (2006)

  41. Foi, A., Katkovnik, V., Egiazarian, K.: Pointwise shape adaptive DCT for high quality denoising and deblocking og grayscale and color images. IEEE Trans. Image Process., vol. 16, No. 5, May (2007)

  42. Bruni, V., Piccoli, B., Vitulano, D.: Wavelet time-scale dependencies for signal and image compression. In: Proceedings of IEEE International Conference ISPA 2005, Zagreb, pp. 105–110 (2005)

Download references

Author information

Authors and Affiliations

  1. Istituto per le Applicazioni del Calcolo “M. Picone”, C.N.R., Viale del Policlinico 137, 00161, Rome, Italy

    Vittoria Bruni, Benedetto Piccoli & Domenico Vitulano

Authors
  1. Vittoria Bruni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benedetto Piccoli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Domenico Vitulano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Domenico Vitulano.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bruni, V., Piccoli, B. & Vitulano, D. A fast computation method for time scale signal denoising. SIViP 3, 63–83 (2009). https://doi.org/10.1007/s11760-008-0060-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-008-0060-9

Keywords

Search

Navigation