Skip to main content

Higher order feasible building blocks for lattice structure of multidimensional linear phase biorthogonal filter banks

Multidimensional Systems and Signal Processing volume 28, pages 637–655 (2017)Cite this article

Abstract

A multidimensional (MD) linear phase biorthogonal filter bank (LPBOFB) with higher order feasible (HOF) building blocks is reported. Basically, there are two ways to design filter banks with large filter supports. One way is to use a cascade of degree-1 building blocks, and the other way is to use a cascade of order-1 building blocks. Unfortunately, both methods have high implementation costs in terms of the number of parameters, especially for the multidimensional case. A previously reported HOF building block has now been applied to MD LPBOFBs. Their generalized structural design supports both an even and odd number of channels. It is shown that the HOF structure cannot be factored into a cascade of order-1 building blocks. The proposed MD LPBOFB has larger filters and uses fewer building blocks than the traditional degree-1 and order-1 structures.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Notes

  1. Nine-channel 2-D LPBOFBs with an order-1 structure which has 144 parameters could not be designed in our computers because of out of memory.

References

  • Bamberger, R. H., & Smith, M. J. T. (1992). A filter bank for the directional decomposition of images: Theory and design. Transactions on Signal Processing, 40(4), 882–893.

    Article  Google Scholar 

  • Chen, Y., Adams, M. D., & Lu, W. S. (2007). Design of optimal quincunx filter banks for image coding. EURASIP Journal on Advances Signal Processing, 2007, 83858. doi:10.1155/2007/83858.

  • de Querioz, R. L., Nguyen, T. Q., & Rao, K. R. (1996). The GenLOT: Generalized linear phase lapped orthogonal transform. IEEE Transactions on Signal Processing, 44, 497–507.

    Article  Google Scholar 

  • Gan, L., & Ma, K.-K. (2001). A simplified lattice factorization for linear-phase perfect reconstruction filter bank. IEEE Signal Processing Letters, 8, 207–209.

    Article  Google Scholar 

  • Gan, L., Ma, K.-K., Nguyen, T. Q., Tran, T. D., & de Queiroz, R. L. (2002). On the completeness of the lattice factorization for linear-phase perfect reconstruction filter banks. IEEE Signal Processing Letters, 9(4), 133–136.

    Article  Google Scholar 

  • Gao, X., Li, B., & Xiao, F. (2013). Lattice structure for generalized-support multidimensional linear phase perfect reconstruction filter bank. IEEE Transactions on Image Processing, 22(12), 4853–4864.

    Article  MathSciNet  Google Scholar 

  • Karlsson, G., & Vetterli, M. (1990). Theory of two-dimensional multirate filter banks. IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(6), 925–937.

    Article  Google Scholar 

  • Kumar, R., Chen, Y., & Amaratunga, K. (2006). Lapped unimodular transforms: Lifting factorization and structual regularity. IEEE Transactions on Signal Processing, 54(3), 921–931.

    Article  Google Scholar 

  • Law, K. L., Fossum, R. M., & Do, M. N. (2009). Generic invertibility of multidimensional FIR filter banks and MIMO systems. IEEE Transactions on Signal Processing, 57(11), 4282–4291.

    Article  MathSciNet  Google Scholar 

  • Lu, Y. M., & Do, M. N. (2007). Multidimensional directional filter banks and surfacelets. IEEE Transactions on Image Processing, 16(4), 918–931.

    Article  MathSciNet  Google Scholar 

  • Makur, A., Muthuvel, A., & Reddy, P. V. (2004). Eigenstructure approach for complete characterization of linear-phase FIR perfect reconstruction analysis length 2m filterbanks. IEEE Transactions on Signal Processing, 52(6), 1801–1804.

    Article  Google Scholar 

  • Malvar, H. S., & Staelin, D. H. (1989). The LOT: Transform coding without blocking effects. IEEE Transactions on Acoustics, Speech, and Signal Processing, 37(4), 553–559.

    Article  Google Scholar 

  • Muramatsu, S., Dandan, H., Kobayashi, T., & Kikuchi, H. (2012). Directional lapped orthogonal transform: Theory and design. IEEE Transactions on Image Processing, 21(5), 2434–2448.

    Article  MathSciNet  Google Scholar 

  • Muramatsu, S., & Kiya, H. (1996). A new design method of linear-phase paraunitary filter banks with an odd number of channels. Proceedings of EUCIPCO, 1, 73–76.

    Google Scholar 

  • Muramatsu, S., Yamada, A., & Kiya, H. (1999). A design method of multidimensional liner-phase paraunitary filter banks with a lattice structure. IEEE Transactions on Signal Processing, 47, 690–700.

    Article  Google Scholar 

  • Muthuvel, A., & Makur, A. (2001). Eigenstructure approach for characterization of FIR PR filterbanks with order one polyphase. IEEE Transactions on Signal Processing, 49(10), 2283–2291.

    Article  Google Scholar 

  • Nguyen, T. T., & Oraintara, S. (2005). Multiresolution direction filterbanks: Theory, design, and applications. IEEE Transactions on Signal Processing, 53(10), 3895–3905.

    Article  MathSciNet  Google Scholar 

  • Nguyen, T. T., & Oraintara, S. (2005). Multidimensional filter banks design by direct optimization. ISCAS, 2, 1090–1093.

    Google Scholar 

  • Oraintara, S., & Nguyen, T. Q. (1997). Multidimensional 2-channel PR filter banks. Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers, 2, 1269–1273.

    Google Scholar 

  • Oraintara, S., Tran, T. D., & Nguyen, T. Q. (2003). A class of regular biorthogonal linear-phase filterbanks: Theory, structure, and application in image coding. IEEE Transactions on Signal Processing, 51(12), 3220–3235.

    Article  MathSciNet  Google Scholar 

  • Phoong, S. M., & Lin, Y. P. (2002). Lapped unimodular transform and its factorization. IEEE Transactions on Signal Processing, 50(11), 2695–2701.

    Article  Google Scholar 

  • Soman, A. K., & Vaidyanathan, P. P. (1993). Coding gain in paraunitary analysis/synthesis systems. IEEE Transactions on Signal Processing, 41(5), 1824–1835.

    Article  MATH  Google Scholar 

  • Soman, A. K., Vaidyanathan, P. P., & Nguyen, T. Q. (1993). Linear phase paraunitary filter banks: Theory, factorizations and designs. IEEE Transactions on Signal Processing, 41(12), 3480–3496.

    Article  MATH  Google Scholar 

  • Strang, G., & Nguyen, T. Q. (1996). Wavelets and filter banks. Wellesley-Cambridge, MA: Norwell.

    MATH  Google Scholar 

  • Tanaka, Y., Ikehara, M., & Nguyen, T.-Q. (2008). A lattice structure of biorthogonal linear-phase filter banks with higher order feasible building blocks. IEEE Transactions on Circuits and Systems, 55–I, 2122–2331.

    MathSciNet  Google Scholar 

  • Tanaka, Y., Ikehara, M., & Nguyen, T. Q. (2009). Higher-order feasible building blocks for lattice structure of oversampled linear-phase perfect reconstruction filter banks. Signal Processing, 89, 1694–1703.

    Article  MATH  Google Scholar 

  • Tran, T. D., de Queiroz, R. L., & Nguyen, T. Q. (2000). Linear-phase perfect reconstruction filter bank: Lattice structure, design, and application in image coding. IEEE Transactions on Signal Processing, 48(1), 133–147.

    Article  Google Scholar 

  • Vaidyanathan, P. P. (1993). Multirate systems and filter banks. Upper Saddle River, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Vaidyanathan, P. P., & Chen, T. (1995). Role of anticausal inverses in multirate filter-banks-part II: The FIR case, factorizations, and biorthogonal lapped transforms. IEEE Transactions on Signal Processing, 43(5), 1103–1115.

    Article  Google Scholar 

  • Vetterli, M., & Kovačevic, J. (1995). Wavelets and subband coding. Upper Saddle River, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Xu, Z., & Makur, A. (2008). On the existence of compelete order-one lattice for linear phase perfect reconstruction filter banks. IEEE Signal Processing Letters, 15, 345–348.

    Article  Google Scholar 

  • Xu, Z., & Makur, A. (2009). On the arbitrary-length M-channel linear phase perfect reconstruction filter banks. IEEE Transactions on Signal Processing, 57(10), 4118–4123.

    Article  MathSciNet  Google Scholar 

  • Yoshida, T., Kyochi, S., & Ikehara, M. (2010). A simplified lattice structure of two-dimensional generalized lapped orthogonal transform (2-D GenLOT) for image coding. In Proceedings of 17th IEEE ICIP, pp. 349–352.

Download references

Acknowledgments

This work was supported in part by MIC SCOPE Grant Number 142103007.

Author information

Authors and Affiliations

  1. The Graduate School of BASE, Tokyo University of Agriculture and Technology, Koganei, Tokyo, 184-8588, Japan

    Ami Hamamoto, Masaki Onuki & Yuichi Tanaka

Authors
  1. Ami Hamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Masaki Onuki
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuichi Tanaka
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ami Hamamoto.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hamamoto, A., Onuki, M. & Tanaka, Y. Higher order feasible building blocks for lattice structure of multidimensional linear phase biorthogonal filter banks . Multidim Syst Sign Process 28, 637–655 (2017). https://doi.org/10.1007/s11045-015-0364-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11045-015-0364-1

Keywords

  • Lattice structure
  • Multidimensional filter banks
  • Higher order feasible (HOF) building blocks
  • Linear phase
  • Perfect reconstruction