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Ridgelets Frame

  • Conference paper
Image Analysis and Recognition (ICIAR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3211))

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Abstract

In this paper, a new system called ridgelets frame in L2 (R2) is constructed. To construct the new system, we use other orthonormal wavelet rather than Meyer wavelet, which was used in the construction of orthonormal ridgelets by Donoho. Due to the losing of two special closure properties of Meyer wavelet, the new system is a tight frame with frame bound 1 instead of orthonormal basis for L2 (R2). As an example, we demonstrate the potential power of the new constructed system by showing its ability of recovering the line structure in images in the presence of noise.

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References

  1. Donoho, D.L.: Orthonormal Ridgelets and Linear Singularities. SIAM J. Math Anal. 5, 1062–1099 (2000)

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  2. Flesia, A.G., Helor, H.A., Averbuch, E.J., Candès, E.J., Coifman, R.R., Donoho, D.L.: Digital Implementation of Ridgelet Packets. Stanford Uni. Stanford, CA, Tech. Rep. (2002)

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  3. Deans, S.R.: The Radon Transform and Some of Its Applications. Wiley, New York (1983)

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  4. Candès, E.J.: Monoscale Ridgelets for the Representation of Images with Edges. Dept. Statist., Stanford Univ., Stanford, CA, Tech. Rep. (1999)

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  5. Candès, E.J., Donoho, D.L.: Curvelets—a Surprisingly Effective Nonadaptive Representation for Objects with Edges. In: Cohen, A., Rabut, C., Schumaker, L.L. (eds.) Curve and Surface Fitting, Van-derbilt Univ. Press, Nashville (1999)

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Author information

Authors and Affiliations

  1. National Key Lab for Radar Signal Processing and Institute of Intelligent, Information Processing, Xidian University, 710071, Xi’an, China

    Tan Shan & Licheng Jiao

  2. College of Science, Xidian University, 710071, Xi’an, China

    Xiangchu Feng

Authors
  1. Tan Shan
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  2. Licheng Jiao
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  3. Xiangchu Feng
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Editor information

Editors and Affiliations

  1. FEUP - Faculdade de Engenharia, Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal

    Aurélio Campilho

  2. Electrical and Computer Engineering Department, University of Waterloo,  

    Mohamed Kamel

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© 2004 Springer-Verlag Berlin Heidelberg

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Cite this paper

Shan, T., Jiao, L., Feng, X. (2004). Ridgelets Frame. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2004. Lecture Notes in Computer Science, vol 3211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30125-7_60

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  • DOI: https://doi.org/10.1007/978-3-540-30125-7_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23223-0

  • Online ISBN: 978-3-540-30125-7

  • eBook Packages: Springer Book Archive

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