Skip to main content

Image Denoising by a Novel Digital Curvelet Reconstruction Algorithm

  • Conference paper
Book cover Wavelet Analysis and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

  • 2986 Accesses

Abstract

For an anisotropic image, wavelets lose their effects on singularity detection because discontinuities across edges are spatially distributed. Based on the idea of curvelet, a new digital curvelet reconstruction algorithm is proposed. Our algorithm provides sparser representations and keeps low computational complexity. When applying it to the image denoising, much better results than the original algorithm are obtained.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. E. J. Candes and D. L. Donoho, Curvelets—A Surprising Effective Nonadaptive Representation For Objects With Edges. Curve and Surface Fitting: Saint-Malo 1999, A. Cohen, C. Rabut, and L. Schumaker, eds., Vanderbilt University Press, (Nashville, TN), 1999.

    Google Scholar 

  2. D. L. Donoho, Orthonormal Ridgelet and Linear Singularities. SIAM J. Math Anal., 31(5), 1062–1099, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. L. Donoho and M.R. Duncan, Digital curvelet Transform: Strategy, Implementation and Experiments. Proc. SPIE, 4056, 12–29, 2000.

    Article  Google Scholar 

  4. J. L. Starck, E. J. Candes, D. L. Donoho, The Curvelet Transform for Image Denoising. IEEE Trans. Image Processing, 11(6), 670–684, 2002.

    Article  MathSciNet  Google Scholar 

  5. D. L. Donoho and Ana Georgina Flesia, Digital Ridgelet Transform based on True Ridge Functions. http://www.stat.Stanford.edu/donoho/Report.

    Google Scholar 

  6. A. Averbuch, R. R. Coifman, D.L. Donoho, M. Israeli, J. Walden, Fast Slant Stack: A notion of Radon Transform for Data in a Cartesian Grid which is Rapidly Computible, Algebraically Exact, Geometrically Faithful and Invertible. http://wwwstat.stanford.edu/ beamlab

    Google Scholar 

  7. K. Grochenig, Acceleration of Frame Algorithm. IEEE Trans. Signal Processing, 41(12), 3331–3340, 1993.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Birkhäuser Verlag Basel/Switzerland

About this paper

Cite this paper

Bai, J., Feng, XC. (2006). Image Denoising by a Novel Digital Curvelet Reconstruction Algorithm. In: Qian, T., Vai, M.I., Xu, Y. (eds) Wavelet Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7778-6_19

Download citation

Publish with us

Policies and ethics