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A general biorthogonal wavelet based on Karhunen–Loéve transform approximation

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Abstract

The lifting style biorthogonal wavelet implementation has a nice property of enabling flexible design; it is immediately reversible and has a simple relation to subband filters. In this work, we present a general wavelet prediction (P) and update (U) filters of two-channel lifting structures. A previous research of the author introduced signal-specific wavelets, which minimizes the difference between block wavelet transform matrix of the wavelet and the Karhunen–Loéve transform of a stochastic process with certain autocorrelation sequence. This research introduces a general wavelet, which can work on any stochastic process. Numerical results are provided in terms of the filter coefficients and experimental performances on 16 test images.

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References

  1. Calderbank, R., Daubechies, I., Sweldens, W., Yeo, B.L.: Wavelet transforms that map integers to integers. Appl. Comput. Harmon. Anal. 5(3), 332–369 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Cetin, A.E., Gerek, Ö.N., Ulukus, S.: Block wavelet transforms for image coding. IEEE Trans. Circuits Syst. Video Technol. 3, 433–435 (1993)

  3. Cohen, A., Daubechies, I., Feauveau, J.C.: Biorthogonal bases of compactly supported wavelets. Commun. Pure Appl. Math. 45(5), 485–560 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. Dogan, M., Gerek, Ö.N.: Performance analysis of QMF filters obtained by the inverse block wavelet transform. In: IKECCO International Conference on Electronics and Computer 2008. Bishkek, Kyrgyzstan (2008)

  5. Dogan, M., Gerek, Ö.N.: Subband decomposition filter bank design from the inverse block wavelet transform using LMS optimization. In: IWW 2008, International Workshop III: Mini Symposium on Applications of Wavelets to Real World Problems. Istanbul, Turkey (2008)

  6. Dogan, M., Gerek, Ö.N.: A signal-specific QMF bank design technique using Karhunen-Loeve transform approximation. EURASIP J. Adv. Signal Process. (2011). doi:10.1155/2011/753572

  7. Gerek, Ö.N., Cetin, A.E.: Adaptive polyphase subband decomposition structures for image compression. IEEE Trans. Image Process. 9(10), 1649–1660 (2000)

    Article  Google Scholar 

  8. Gerek, Ö.N., Cetin, A.E.: A 2-d orientation-adaptive prediction filter in lifting structures for image coding. IEEE Trans. Image Process. 15(1), 106–111 (2006)

    Article  Google Scholar 

  9. Kale, M.C., Atac, G., Gerek, Ö.N.: A biorthogonal wavelet design technique using Karhunen–Loéve transform approximation. Digit. Signal Process. (2015). doi:10.1016/j.dsp.2015.06.002

  10. Kale, M.C., Gerek, Ö.N.: Lifting wavelet design by block wavelet transform inversion. In: ICASSP, pp. 2619–2623 (2014)

  11. Sweldens, W.: The lifting scheme: a custom-design construction of biorthogonal wavelets. Appl. Comput. Harmon. Anal. 3, 186–200 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sweldens, W.: The lifting scheme: a construction of second generation wavelets. SIAM J. Math. Anal. 29(2), 511–546 (1997)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Eskişehir Osmangazi University, Eskişehir, Turkey

    Mehmet Cemil Kale

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  1. Mehmet Cemil Kale
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Correspondence to Mehmet Cemil Kale.

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Kale, M.C. A general biorthogonal wavelet based on Karhunen–Loéve transform approximation. SIViP 10, 791–794 (2016). https://doi.org/10.1007/s11760-016-0860-2

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  • DOI: https://doi.org/10.1007/s11760-016-0860-2

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