Skip to main content
SpringerLink
Log in

Image Denoising using Tight-Frame Dual-Tree Complex Wavelet Transform

  • Conference paper
  • First Online:
Machine Intelligence and Signal Analysis

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 748))

  • 1283 Accesses

Abstract

In this paper, we propose a new approach to design the 1D biorthogonal filters of dual-tree complex wavelet transform (DTCWT) in order to have almost tight-frame characteristics. The proposed approach involves use of triplet halfband filter bank (THFB) and optimization of free variables obtained using factorization of generalized halfband polynomial (GHBP) to design the filters of two trees of DTCWT. The wavelet functions associated with these trees exhibit better analyticity in terms of qualitative and quantitative measures. Transform-based image denoising using the proposed filters shows comparable performance to the best performing orthogonal wavelet filters.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Similar content being viewed by others

References

  1. Anantrasirichai, N., Achim, A., Kingsbury, N.G., Bull, D.R.: Atmospheric turbulence mitigation using complex wavelet-based fusion. IEEE Trans. Image Process. 22(6), 2398–2408 (2013)

    Article  MathSciNet  Google Scholar 

  2. Ansari, R., Kim, C.W., Dedovic, M.: Structure and design of two-channel filter banks derived from a triplet of halfband filters. IEEE Trans. Circuits Syst. II Analog. Digit. Signal Process. 46(12), 1487–1496 (1999)

    Article  Google Scholar 

  3. Asikuzzaman, M., Alam, M.J., Lambert, A.J., Pickering, M.R.: Robust DT-CWT based DIBR 3D video watermarking using chrominance embedding. IEEE Trans. Multimed. 18(9), 1733–1748 (2016)

    Article  Google Scholar 

  4. Burrus, C.S.: Bases, orthogonal bases, biorthogonal bases, frames, tight frames, and unconditional bases. https://cnx.org/contents/Es1rEfS5@4/Bases-Orthogonal-Bases-Biortho. Accessed 24 April 2017

  5. Donoho, D.L., Johnstone, I.M.: Ideal spatial adaptation by wavelet shrinkage. Biometrica 81(3), 425–455 (1994). Aug

    Article  MathSciNet  Google Scholar 

  6. Fierro, M., Ha, H.G., Ha, Y.H.: Noise reduction based on partial-reference, dual-tree complex wavelet transform shrinkage. IEEE Trans. Image Process. 22(5), 1859–1872 (2013)

    Article  MathSciNet  Google Scholar 

  7. Kingsbury, N.: Image processing with complex wavelets. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 357(1760), 2543–2560 (1999)

    Article  Google Scholar 

  8. Kingsbury, N.: A dual-tree complex wavelet transform with improved orthogonality and symmetry properties. In: ICIP. vol. 2, pp. 375–378. IEEE, USA (2000)

    Google Scholar 

  9. Kingsbury, N.: Complex wavelets for shift invariant analysis and filtering of signals. Appl. Comput. Harmon. Anal. 10(3), 234–253 (2001)

    Article  MathSciNet  Google Scholar 

  10. Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Pearson Higher Education (2010)

    Google Scholar 

  11. Patil, B.D., Patwardhan, P.G., Gadre, V.M.: On the design of FIR wavelet filter banks using factorization of a halfband polynomial. IEEE Signal Process. Lett. 15, 485–488 (2008)

    Article  Google Scholar 

  12. Rabbani, H., Gazor, S.: Video denoising in three-dimensional complex wavelet domain using a doubly stochastic modelling. IET Image Process. 6(9), 1262–1274 (2012)

    Article  MathSciNet  Google Scholar 

  13. Selesnick, I.W. http://eeweb.poly.edu/iselesni/WaveletSoftware/. Accessed 08 April 2014

  14. Selesnick, I.W.: Hilbert transform pairs of wavelet bases. IEEE Signal Process. Lett. 8(6), 170–173 (2001)

    Article  Google Scholar 

  15. Selesnick, I.W.: The design of approximate Hilbert transform pairs of wavelet bases. IEEE Trans. Signal Process. 50(5), 1144–1152 (2002)

    Article  MathSciNet  Google Scholar 

  16. Selesnick, I.W., Baraniuk, R.G., Kingsbury, N.C.: The dual-tree complex wavelet transform. IEEE Signal Process. Mag. 22(6), 123–151 (2005)

    Article  Google Scholar 

  17. Shi, H., Luo, S.: A new scheme for the design of Hilbert transform pairs of biorthogonal wavelet bases. EURASIP J. Adv. Signal Process. 2010, 98 (2010)

    Article  Google Scholar 

  18. Tay, D.B.H.: Designing Hilbert-pair of wavelets: recent progress and future trends. In: 6th International Conference on Information Communication and Signal Process. pp. 1–5. IEEE, USA (2007)

    Google Scholar 

  19. Tay, D.B., Kingsbury, N.G., Palaniswami, M.: Orthonormal Hilbert-pair of wavelets with (almost) maximum vanishing moments. IEEE Signal Process. Lett. 13(9), 533–536 (2006)

    Article  Google Scholar 

  20. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)

    Article  Google Scholar 

  21. Yu, R., Ozkaramanli, H.: Hilbert transform pairs of biorthogonal wavelet bases. IEEE Trans. Signal Process. 54(6), 2119–2125 (2006)

    Article  Google Scholar 

  22. Zhang, L., Zhang, L., Mou, X., Zhang, D.: FSIM: a feature similarity index for image quality assessment. IEEE Trans. Image Process. 20(8), 2378–2386 (2011)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. DA-IICT, Gandhinagar, Gujarat, India

    Shrishail S. Gajbhar & Manjunath V. Joshi

  2. WIT, Solapur, Maharashtra, India

    Shrishail S. Gajbhar

Authors
  1. Shrishail S. Gajbhar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manjunath V. Joshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shrishail S. Gajbhar .

Editor information

Editors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Madhya Pradesh, India

    M. Tanveer

  2. Discipline of Electrical Engineering, Indian Institute of Technology Indore, Simrol, Madhya Pradesh, India

    Ram Bilas Pachori

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Gajbhar, S.S., Joshi, M.V. (2019). Image Denoising using Tight-Frame Dual-Tree Complex Wavelet Transform. In: Tanveer, M., Pachori, R. (eds) Machine Intelligence and Signal Analysis. Advances in Intelligent Systems and Computing, vol 748. Springer, Singapore. https://doi.org/10.1007/978-981-13-0923-6_55

Download citation

Publish with us

Policies and ethics

Search

Navigation