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Multi-scale Geometric Analysis and Its Application of De-noising

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Recent Advances in Computer Science and Information Engineering

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 126))

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Abstract

The essence of multi-scale geometric analysis is to achieve optimal approximation of signal interested. This paper firstly introduces the backgrounds and recent developments of the subject, unveil the impetus behind this root causes. Finally we compare the differences of wavelet transform, contourlet transform and curvelet transform in suppression of random noise, and through practical experiments we confirm that multi-scale geometric analysis are better (sparser) than wavelet in approximating multidimensional signal of interested.

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References

  1. Stein, E.M.: Fourier analysis: an introduction, pp. 5–171. Princeton University Press (2006)

    Google Scholar 

  2. Xinda, Z., Zheng, B.: Non-stationary signal analysis, pp. 17–178. National defense industry Press (1998)

    Google Scholar 

  3. Gabor, D.: Theory of communication. Journal of Institute for Electrical Engineering 93, 429–457 (1946)

    Google Scholar 

  4. Mallat, S.: A Wavelet Tour of Signal Processing, 2nd edn., pp. 67–216. Academic Press (1999)

    Google Scholar 

  5. Mallat, S.: A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans., PAMI 11(7), 674–693 (1989)

    Article  MATH  Google Scholar 

  6. Sarkar, T.K., Su, C.: A tutorial on wavelets from an electrical engineering perspective, Part 2: the continuous case. IEEE Antennas & Propagation Magazine 40(6), 36–48 (1988)

    Article  Google Scholar 

  7. Daubechies, I.: Orthonormal bases of compactly supported wavelets. Comm. Pure and Applied Math. 41, 909–996 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Aldroubi, A., Laine, A.F., Unser, M.A.: Wavelet applications in signal and image proc-essing VI. In: Proc. SPIE, vol. 3458, pp. 24–37 (1998)

    Google Scholar 

  9. Donoho, D.L., Vetterli, M., DeVore, R.A., Daubechies, I.: Data compression and harmonic analysis. IEEE Trans. Inform. 44(6), 2435–2476 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jiao, L., Tan, S.: Development and Prospect of Image Multiscale Geometric Analysis. Chinese Journal of Electronics 31, 1975–1981 (2003)

    Google Scholar 

  11. Pennec, E.L., Mallat, S.: Sparse geometric image representation with bandelets. IEEE Trans. on Image Processing 14(4), 423–438 (2005)

    Article  Google Scholar 

  12. Hubel, D.H., Wiesel, T.N.: Receptive fields, binocular interaction and functional ar-chitecture in the cat’s visual cortex. Journal of Physiology 160, 106–154 (1962)

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  14. Pennec, E.L., Mallat, S.: Image compression with Geometrical wavelets. IEEE ICIP, Canada (2000)

    Google Scholar 

  15. Candès, E.J.: Ridgelets: Theory and Applications. Stanford University, California (1998)

    Google Scholar 

  16. Hong, B., Liu, F., Jiao, L.: Linear feature detection based on ridgelet transform. Science in China (E) 33(1), 65–73 (2003)

    Google Scholar 

  17. DeVore, R.A.: Nonlinear approximation. Acta Numer. 7, 51–150 (1998)

    Article  MathSciNet  Google Scholar 

  18. Candès, E.J., Donoho, D.L.: Ridgelets: a key to higher-dimensional intermittency. Phil. Trans. R Soc. Lond. (1999)

    Google Scholar 

  19. Donoho, D.L., Flesia, A.G.: Can recent innovations in harmonic analysis ex-plain key findings in natural image statistics. Computation in Neural Systems 12, 371–393 (2001)

    MATH  Google Scholar 

  20. Candès, E.J., Donoho, D.L.: Curvelets: a surprisingly effective nonadaptive representation for objects with edges, pp. 105–120. Vandebilt University Press, Nashville (2000)

    Google Scholar 

  21. Do, M.N.: Directional multiresolution image representation. Swiss federal institute of technology, Lausanne (2001)

    Google Scholar 

  22. Do, M.N., Vetterli, M.: Contourlets: a directional multiresolution image representation. In: International Conference on Image Process., Rochester (2002)

    Google Scholar 

  23. Candès, E.J., Donoho, D.L.: Curvelets, multiresolution representation and scaling laws. In: Wavelet Applications in Signal and Image Processing (2001)

    Google Scholar 

  24. Candès, E.J., Donoho, D.L.: Fast discrete curvelet transform. Cali-fornia Institute of Technology, California (2005)

    Google Scholar 

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Author information

Authors and Affiliations

  1. College of Science, China University of Petroleum, Beijing, China

    Wu Guoning

  2. College of Geophysics and Information Engineering, China University of Petroleum, Beijing, China

    Cao Siyuan

  3. College of Mechanical and Transportation Engineering, China University of Petroleum, Beijing, China

    Duan Qingquan

Authors
  1. Wu Guoning
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  2. Cao Siyuan
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  3. Duan Qingquan
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Corresponding author

Correspondence to Wu Guoning .

Editor information

Editors and Affiliations

  1. , College of Communication Engineering, Jilin University, Room 313, Building No.1, Changchun, Nanhu Avenue 5372, Jilin, 130012, China, People's Republic

    Zhihong Qian

  2. , Department of Electrical Engineering, The University of Mississippi, Anderson Hall 314, Mississippi, 38677, Mississippi, USA

    Lei Cao

  3. , Department of Electrical and Computer En, Naval Postgraduate School, Rm. 452 Spanagel Bldg. 232, Dyer Road 833, Monterey, 93943-5121, California, USA

    Weilian Su

  4. , Faculty of Computing, London Metropolitan University, Holloway Road 166-220, London, N7 8DB, United Kingdom

    Tingkai Wang

  5. , College of Software, Changchun University of Science and Tech, Changchun, Jilin, 130022, China, People's Republic

    Huamin Yang

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© 2012 Springer-Verlag GmbH Berlin Heidelberg

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Guoning, W., Siyuan, C., Qingquan, D. (2012). Multi-scale Geometric Analysis and Its Application of De-noising. In: Qian, Z., Cao, L., Su, W., Wang, T., Yang, H. (eds) Recent Advances in Computer Science and Information Engineering. Lecture Notes in Electrical Engineering, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25766-7_80

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  • DOI: https://doi.org/10.1007/978-3-642-25766-7_80

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25765-0

  • Online ISBN: 978-3-642-25766-7

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