Skip to main content
SpringerLink
Log in

Design of Biorthogonal Wavelet Filters of DTCWT Using Factorization of Halfband Polynomials

  • Conference paper
  • First Online:
Book cover Computer Vision, Pattern Recognition, Image Processing, and Graphics (NCVPRIPG 2017)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 841))

  • 1385 Accesses

Abstract

In this paper, we propose a new approach for designing the biorthogonal wavelet filters (BWFs) of Dual-Tree Complex Wavelet Transform (DTCWT). Proposed approach provides an effective way to handle the frequency response characteristics of these filters. This is done by optimizing the free variables obtained using factorization of generalized halfband polynomial (GHBP). The designed filters using proposed approach have better frequency response characteristics than those obtained by using binomial spectral factorization approach. Also, their associated wavelets show improved analyticity in terms of qualitative and quantitative measures. Transform-based image denoising using the proposed filters shows better visual as well as quantitative performance.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

References

  1. 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 

  2. 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 

  3. 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 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  11. Chaux, C., Duval, L., Pesquet, J.C.: Image analysis using a dual-tree M-band wavelet transform. IEEE Trans. Image Process. 15(8), 2397–2412 (2006)

    Article  MathSciNet  Google Scholar 

  12. Chaux, C., Pesquet, J.C., Duval, L.: 2D dual-tree complex biorthogonal M-band wavelet transform. In: 2007 IEEE International Conference on Acoustics, Speech and Signal Processing-ICASSP 2007, vol. 3, pp. III-845. IEEE (2007)

    Google Scholar 

  13. Yu, R., Ozkaramanli, H.: Hilbert transform pairs of orthogonal wavelet bases: necessary and sufficient conditions. IEEE Trans. Sig. Process. 53(12), 4723–4725 (2005)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  15. Thiran, J.P.: Recursive digital filters with maximally flat group delay. IEEE Trans. Circ. Theory 18(6), 659–664 (1971)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  17. Daubechies, I., et al.: Ten Lectures on Wavelets, vol. 61. SIAM, Philadelphia (1992)

    Book  Google Scholar 

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

    Article  Google Scholar 

  19. Lightstone, M., Majani, E., Mitra, S.K.: Low bit-rate design considerations for wavelet-based image coding. Multidimension. Syst. Sig. Process. 8(1–2), 111–128 (1997)

    Article  Google Scholar 

  20. Rahulkar, A.D., Patil, B.D., Holambe, R.S.: A new approach to the design of biorthogonal triplet half-band filter banks using generalized half-band polynomials. Signal Image Video Process. 8(8), 1451–1457 (2014)

    Article  Google Scholar 

  21. Selesnick, I.W.: http://eeweb.poly.edu/iselesni/WaveletSoftware/. Accessed 04 Aug 2014

  22. Sendur, L., Selesnick, I.W.: Bivariate shrinkage functions for wavelet-based denoising exploiting interscale dependency. IEEE Trans. Sig. Process. 50(11), 2744–2756 (2002)

    Article  Google Scholar 

  23. 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 

  24. 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

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. Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Renu Rameshan

  2. Indraprastha Institute of Information Technology, New Delhi, India

    Chetan Arora

  3. Indian Institute of Technology, New Delhi, India

    Sumantra Dutta Roy

Rights and permissions

Reprints and permissions

Copyright information

© 2018 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. (2018). Design of Biorthogonal Wavelet Filters of DTCWT Using Factorization of Halfband Polynomials. In: Rameshan, R., Arora, C., Dutta Roy, S. (eds) Computer Vision, Pattern Recognition, Image Processing, and Graphics. NCVPRIPG 2017. Communications in Computer and Information Science, vol 841. Springer, Singapore. https://doi.org/10.1007/978-981-13-0020-2_14

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-0020-2_14

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0019-6

  • Online ISBN: 978-981-13-0020-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation