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Time-Scale Similarities for Robust Image De-noising

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Abstract

This paper presents a novel image denoising algorithm, namely Atomic Non Local Means (ANL-means), that looks for similarities in the time-scale domain. To this aim, wavelet details are approximated by linear combinations of predefined atoms, whose centers of mass trace trajectories in the time-scale plane (from fine to coarse scales). These trajectories depend on the mutual distance between not isolated singularities, their different decay along scales and their amplitude ratio. These three parameters have proved to be useful in catching image self-similarities and in the implementation of a robust NL-means based denoising algorithm. ANL-means is able to reach and often outperform the most powerful and recent NL-means based de-noising schemes in terms of both mean square error and visual quality.

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References

  1. Azzabou, N., Paragios, N., Guichard, F.: Image denoising based on adapted dictionary computation. In: Proc. of ICIP 2007, vol. III, pp. 109–112 (2007)

    Google Scholar 

  2. Balster, E.J., Zheng, Y.F., Ewing, R.L.: Feature-based wavelet shrinkage algorithm for image denoising. IEEE Trans. Image Process. 14(12), 2024–2039 (2005)

    Article  Google Scholar 

  3. Bruni, V., Vitulano, D.: Wavelet based signal denoising via simple singularities approximations, signal processing. Elsevier Sci. 86, 859–876 (2006)

    MATH  Google Scholar 

  4. Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms with a new one. Multiscale Model. Simul. 4(2), 490–530 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chang, S.G., Yu, B., Vetterli, M.: Spatially adaptive thresholding with context modeling for image denoising. IEEE Trans. Image Process. 9(1), 1522–1530 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: BM3D image denoising with shape-adaptive principal component analysis. In: SPARS’09—Signal Processing with Adaptive Sparse Structured Representations, Saint-Malo, France, Apr. (2009)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  9. Easley, G.R., Labate, D., Colonna, F.: Shearlet-based total variation diffusion for denoising. IEEE Trans. Image Process. 18(2), 260–268 (2009)

    Article  MathSciNet  Google Scholar 

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

    Google Scholar 

  11. Foi, A., Katkovnik, V., Egiazarian, K.: Pointwise shape adaptive DCT for high quality denoising and deblocking of grayscale and color images. In: Proc. of SPIE—IS & T Electronic Imaging, vol. 6064 (2006)

    Google Scholar 

  12. Guerrero-Colon, J.A., Mancera, L., Portilla, J.: Image restoration using space-variant Gaussian scale mixtures in overcomplete pyramids. IEEE Trans. Image Process. 17(1), 27–41 (2008)

    Article  MathSciNet  Google Scholar 

  13. Kervrann, C., Boulanger, J., Coupè, P.: Bayesian non local mean filter, image redundancy and adaptive dictionaries for noise removal. In: Lecture Notes in Computer Science, Graz, Austria, vol. 4485, pp. 520–532. Springer, Berlin (2007)

    Google Scholar 

  14. Mallat, S., Hwang, W.L.: Singularity detection and processing with wavelets. IEEE Trans. Inf. Theory 38(2), 617–643 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. 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 

  16. 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. 11(5), 545–557 (2002)

    Article  Google Scholar 

  17. Sendur, L., Selesnick, I.W.: Bivariate shrinkage with local variance estimation. IEEE Signal Process. Lett. 9(12), 670–684 (2002)

    Article  Google Scholar 

  18. Wei, J.: Lebesgue Anisotropic Image Denoising. Wiley, New York (2005)

    Google Scholar 

  19. 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 

  20. Do, M.N., Vetterli, M.: The contourlet transform: an efficient directional multiresolution image representation. IEEE Trans. Image Process. 14(12), 2091–2106 (2005)

    Article  MathSciNet  Google Scholar 

  21. Le Pennec, E., Mallat, S.: Sparse geometric image representations with bandelets. IEEE Trans. Image Process. 14(4), 423–438 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  23. Bilcu, R.C., Vehvilainem, M.: Fast non local means for image denoising. In: Proc. of SPIE Digital Photography III, vol. 6502(1) (2007)

    Google Scholar 

  24. Dauwe, A., Goossens, B., Luong, H., Philips, W.: A fast non local image denoising algorithm. In: Proc. of SPIE Electronic Imaging, San Jose, USA, Jan. 2008, vol. 6812 (2008)

    Google Scholar 

  25. Coupé, P., Hellier, P., Prima, S., Kervrann, C., Barillot, C.: 3D wavelet subbands mixing for image denoising. Int. J. Biomed. Imaging (2008). doi:10.1155/2008/590183

  26. Wang, J., Guo, Y., Ying, Y., Liu, Y., Peng, Q.: Fast non-local algorithm for image denoising. In: Proc. of IEEE ICIP, Atlanta, CA, Oct. 2006, pp. 1429–1432 (2006)

    Google Scholar 

  27. Mahmoudi, M., Sapiro, G.: Fast image and video denoising via non local means of similar neighborhoods. IEEE Signal Process. Lett. 12(12), 839–842 (2005)

    Article  Google Scholar 

  28. Tasdizen, T.: Principal neighborhood dictionaries for non-local means image denoising. IEEE Trans. Image Process. 18(12), 2649–2660 (2009)

    Article  MathSciNet  Google Scholar 

  29. Chatterjee, P., Milanfar, P.: A generalization of non-local means via kernel regression. In: Proc. of IS&T/SPIE Conf. on Computational Imaging VI, San Jose, USA, Jan. 2008, vol. 6814 (2008)

    Google Scholar 

  30. Brox, T., Cremers, D.: Iterated nonlocal means for texture restoration. Lect. Notes Comput. Sci. 4485, 13–24 (2007)

    Article  Google Scholar 

  31. Van De Ville, D., Kocher, M.: SURE-based non-local means. IEEE Signal Process. Lett. 16(11), 973–976 (2009)

    Article  Google Scholar 

  32. Goossens, B., Luong, H., Pizurica, A., Philips, W.: An improved non-local denoising algorithm. In: International Workshop on Local and Non-Local Approximation in Image Processing (LNLA2008), Lausanne, Switzerland, Aug. 2008, pp. 25–29 (2008)

    Google Scholar 

  33. Mallat, S.: A Wavelet Tour of Signal Processing. Academic Press, San Diego (1998)

    MATH  Google Scholar 

  34. Bruni, V., Piccoli, B., Vitulano, D.: Fast computation method for time scale signal denoising. In: Signal, Image and Video Processing, vol. 3(1). Springer, London (2009)

    Google Scholar 

  35. 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 

  36. Foi, A., Katkovnik, V., Egiazarian, K.: Pointwise shape adaptive DCT for high quality denoising and deblocking of grayscale and color images. IEEE Trans. Image Process. 16(5), 1395–1411 (2007)

    Article  MathSciNet  Google Scholar 

  37. Luisier, F., Blu, T., Unser, M.: A new SURE approach to image denoising: interscale orthonormal wavelet thresholding. IEEE Trans. Image Process. 16(3), 593–606 (2007)

    Article  MathSciNet  Google Scholar 

  38. Wong, A., Fieguth, P., Clausi, D.: A perceptually adaptive approach to image denoising using anisotropic non-local means. In: Proc. of IEEE ICIP, San Diego, CA, Oct. 2008, pp. 537–540 (2008)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering—Dept. of SBAI, University of Rome La Sapienza, Via A. Scarpa 16, 00161, Rome, Italy

    Vittoria Bruni

  2. Istituto per le Applicazioni del Calcolo “M. Picone”—C.N.R., Via dei Taurini 19, 00185, Rome, Italy

    Domenico Vitulano

Authors
  1. Vittoria Bruni
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  2. Domenico Vitulano
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Correspondence to Vittoria Bruni.

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Bruni, V., Vitulano, D. Time-Scale Similarities for Robust Image De-noising. J Math Imaging Vis 44, 52–64 (2012). https://doi.org/10.1007/s10851-011-0310-2

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  • DOI: https://doi.org/10.1007/s10851-011-0310-2

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