International Journal of Emerging Research in Engineering, Science, and Management
Vol. 1, Issue 1, pp. 11-17, Jan-Mar 2022.
https://doi.org/10.58482/ijeresm.v1i1.3

Design of Biorthogonal Wavelets based on Spline and Spline-like Functions for Image Compression

K Subramanyam

T Ramasri

Assistant Professor, Dept. of ECE, Gokula Krishna College of Engineering, Sullurpet

Professor, Dept. of ECE, Sri Venkateswara University College of Engineering, Tirpati

Abstract: Wavelet theory inspired from Fourier analysis is based on the basis function and its properties. Different wavelets use different basis functions which may better suit to some applications. The properties of basis functions along with their shape and magnification effects the performance of an application. The standard biorthogonal wavelets utilize spline functions for their construction. In this paper first the design procedure of biorthogonal wavelets is presented. Then a modified spline function is proposed. Based on the proposed spline function, three biorthogonal wavelets are designed with different length. The performance of proposed wavelets is analyzed by applying them on to images for SPIHT compression. The simulation results shown that the proposed wavelets have performed well compared to that of standard spline based biorthogonal wavelets.

Keywords: spline-like function, biorthogonality, symmetry, normality.

References:

  1. Abmed and K. R. Rao, “Orthogonal Transforms for Digital Signal Processing”, Springer Press, Berlin, (1975), pp. 1-10.
  2. Shen and I. K. Sethi, “DCT convolution and its application in compressed domain”, IEEE Transactions on Circuits and Systems for Video Technology, vol. 8, no. 8, (1998), pp. 947-952.
  3. X. Hou and X. Yang, “The all phase DFT filter”, Proceedings of the 10th IEEE Digital Signal Processing Workshop and the 2nd IEEE Signal Processing Education Workshop, Pine Mountain, Georgia, USA, (2002), October 13-16, pp. 221-226.
  4. X. Hou, Z. H. Wang and X. Yang, “Design and implementation of all phase DFT digital filter”, Acta Electronica Sinica, vol. 31, no. 4, (2003), pp. 539-543.
  5. X. Hou, “Design and application of the discrete cosine sequency filters”, Journal of Tianjin University (Science and Technology), vol. 32, no. 3, (1999), pp. 324-328.
  6. G. Mallat, “A theory for multiresolution signal decomposition: The wavelet representation”, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 7, (1989), pp. 674-693.
  7. G. Mallat, “Multiresolution approximations and wavelet orthonormal bases of L2(R)”, Transactions of the American Mathematical Society, vol. 315, no. l, (1989), pp. 69-87.
  8. L. Donoho, “De-noising by soft-thresholding”, IEEE Transactions on Information Theory, vol. 41, no. 3, (1995), pp. 613-627.
  9. Taubman, “High performance scalable image compression with EBCOT”, IEEE Transactions on Image Processing, vol. 9, no. 7, (2000), pp. 1158-1170.
  10. Junqiu Wang, Juanfei Li, “Existence and Design of a Kind of Biorthogonal Vector-Valued Wavelets”, IEEE International Conference on Environmental Science and Information Application Technology, vol. 3, 2009.
  11. Jian-Zhong Liu, Zheng-Xin Hou, Cheng-you Wang, “Design and properties of anti-symmetric biorthogonal wavelet filter banks with the same even length”, IEEE International Conference on Wavelet Analysis and Pattern Recognition, 2009.
  12. Manish Sharma, Tarwar Sinrgh, Dinesh Bhati, Vikram Gadre, “Design of two-channel linear phase biorthogonal wavelet filter banks via convex optimization”, IEEE International Conference on Signal Processing and Communications (SPCOM), 2014.
  13. HUANG Jing, LV Bing-qing, “A Feasible Algorithm for Designing Biorthogonal Bivariate Vector-valued Finitely Supported Wavelets”, International Conference on Solid State Devices and Materials Science, ELSEVIER Physics Procedia, 25, 1507 – 1514, 2012.
  14. Delin Hua, Construction of a type of Biorthogonal Binary Wave Functions by Multiresolution Analysis Approach”, International Conference on Solid State Devices and Materials Science, ELSEVIER Physics Procedia, 33, 1346 – 1353, 2012.
  15. Hongli Shi and Shuqian Luo, “A New Scheme for the Design of Hilbert Transform Pairs of Biorthogonal Wavelet Bases”, EURASIP Journal on Advances in Signal Processing 2010.
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