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Application of symmetric orthogonal multiwavelets and prefilter technique for image compression
Keywords:
Image compression, Multiwavelets, Prefilter techniqueAbstract
Multiwavelets are new addition to the body of wavelet theory. There are many types of symmetric multiwavelets such as Geronimo-Hardin-Massopust (GHM) and Chui-Lian (CL) multiwavelets. However, the matrix filter generating the GHM system multiwavelets does not satisfy the symmetric property. For this reason, this paper presents a new method to construct the symmetric orthogonal matrix filter, which leads to the symmetric orthogonal multiwavelets (SOM). Moreover, we analyze the prefilter technique, corresponding to the symmetric orthogonal matrix filter, to get a good combining frequency response. To prove the good property of SOM in image compression application, we compared the compression effect with other writers' work, which was in published literature.
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References
[1] Goodman T. N. T, Lee S. L, and Tang, “Wavelets in wandering subspaces” Trans. Amer. Math. Soc, 1993, Vol. 338, No. 1: 639-654.
[2] Goodman T. N. T and Lee S. L, “Wavelets of multiplicity r,” Trans. Amer. Math. Soc, 1994, Vol. 342, No. 1: 307-324.
[3] Jia R. Q, Remeschneider S, and Zhou D. X, “Vector subdivision schemes and multiple wavelet” Elsevier Math. Comp, 1998, 67: 1533-1563.
[4] Chui C.K and Lian J, “A study on orthonormal multiwavelets,” Appl. Numer. Math, 1996, Vol. 20: 273-298.
[5] Hong D and Wu A, “Orthgonal multiwavelets of multiplicity four” Elsevier Math.Comp, 2000, 40: 1153-1169.
[6] Tham J. Y, Shen L, and Lee S. L, “A general approch for analysis and application of discrete multiwavelet tansforms” IEEE Trans. Signal Processing, 2000, Vol. 48, No. 2: 457-464.
[7] Strela V and Heller P.N, “The application of multiwavelet filterbanks to image processing,” IEEE Trans. Image Processing, 2000, Vol.8, No.4: .548-563, 1999.
[8] Cotronei M, Lazzaro D, Montefusco L. B, and Puccio L, “Image Compression Through Embedded Multiwavelet Transform Coding,” IEEE Trans. Image Processing, 2000, Vol. 9, No. 2: 184-189.
[9] Strang G and Strela V, “Short wavelets and matrix dilation equations,” IEEE Trans. Signal Processing, 1995, Vol. 43: 108-115.
[10] Donivan G. C, Geronimo J. S, and Hardin D. P, “Orthogonal polynomials and the contruction of piecewise polynomial smooth wavelets” Siam J. Math. Anal, 1999, Vol. 30, No. 5: 1029-1056
[11] Jiang Q, “Orthogonal multiwavelets with optium time-frequency resolution,” IEEE Trans. Signal Processing, 1998, Vol. 46, No.6: 830-844.
[12] Xia X. G, “A new prefilter design for discrete multiwavelet transforms,” IEEE Trans. Signal Processing, 1998, Vol. 46, No.4: 1558-1570.
[13] Xia X. G, Geronimo J. S, and Hardin D. P, “Design of prefilters for discrete multiwavelet transforms,” IEEE Trans. Signal Processing, 1996, Vol. 44, No. 1: 25-35.
[14] Hardin D.P and Roach D. W, “Multiwavelet prefilter I: Orthogonal prefilters preserving approximation order p d 2 ,” IEEE Trans. Circuits Syst. II, 1998, Vol. 45, No.8: 1106-1112.
[15] A. Said, W.A.Pearlman. “A new fast and efficient image codec based on set partitioning in hierachical trees”, IEEE Transactions on Circuits and Systems for Video technology, 6 (3): 243-250, 1996
[16] Bing-Bing Chai, Jozsef Vass, and Xinhua Zhuang. “Sinificance-linked connected component analysis for wavelet image coding”, IEEE Transactions on Image Processing, 1999, 8(6): 774-783
[17] S. D. Servetto, K. Ramchandran, and M.T.Orchard, “ Image coding based on a morphological representation of wavelet data”, IEEE Trans. Image Processing, 8(9), pp. 1161-1174. 1999.
[2] Goodman T. N. T and Lee S. L, “Wavelets of multiplicity r,” Trans. Amer. Math. Soc, 1994, Vol. 342, No. 1: 307-324.
[3] Jia R. Q, Remeschneider S, and Zhou D. X, “Vector subdivision schemes and multiple wavelet” Elsevier Math. Comp, 1998, 67: 1533-1563.
[4] Chui C.K and Lian J, “A study on orthonormal multiwavelets,” Appl. Numer. Math, 1996, Vol. 20: 273-298.
[5] Hong D and Wu A, “Orthgonal multiwavelets of multiplicity four” Elsevier Math.Comp, 2000, 40: 1153-1169.
[6] Tham J. Y, Shen L, and Lee S. L, “A general approch for analysis and application of discrete multiwavelet tansforms” IEEE Trans. Signal Processing, 2000, Vol. 48, No. 2: 457-464.
[7] Strela V and Heller P.N, “The application of multiwavelet filterbanks to image processing,” IEEE Trans. Image Processing, 2000, Vol.8, No.4: .548-563, 1999.
[8] Cotronei M, Lazzaro D, Montefusco L. B, and Puccio L, “Image Compression Through Embedded Multiwavelet Transform Coding,” IEEE Trans. Image Processing, 2000, Vol. 9, No. 2: 184-189.
[9] Strang G and Strela V, “Short wavelets and matrix dilation equations,” IEEE Trans. Signal Processing, 1995, Vol. 43: 108-115.
[10] Donivan G. C, Geronimo J. S, and Hardin D. P, “Orthogonal polynomials and the contruction of piecewise polynomial smooth wavelets” Siam J. Math. Anal, 1999, Vol. 30, No. 5: 1029-1056
[11] Jiang Q, “Orthogonal multiwavelets with optium time-frequency resolution,” IEEE Trans. Signal Processing, 1998, Vol. 46, No.6: 830-844.
[12] Xia X. G, “A new prefilter design for discrete multiwavelet transforms,” IEEE Trans. Signal Processing, 1998, Vol. 46, No.4: 1558-1570.
[13] Xia X. G, Geronimo J. S, and Hardin D. P, “Design of prefilters for discrete multiwavelet transforms,” IEEE Trans. Signal Processing, 1996, Vol. 44, No. 1: 25-35.
[14] Hardin D.P and Roach D. W, “Multiwavelet prefilter I: Orthogonal prefilters preserving approximation order p d 2 ,” IEEE Trans. Circuits Syst. II, 1998, Vol. 45, No.8: 1106-1112.
[15] A. Said, W.A.Pearlman. “A new fast and efficient image codec based on set partitioning in hierachical trees”, IEEE Transactions on Circuits and Systems for Video technology, 6 (3): 243-250, 1996
[16] Bing-Bing Chai, Jozsef Vass, and Xinhua Zhuang. “Sinificance-linked connected component analysis for wavelet image coding”, IEEE Transactions on Image Processing, 1999, 8(6): 774-783
[17] S. D. Servetto, K. Ramchandran, and M.T.Orchard, “ Image coding based on a morphological representation of wavelet data”, IEEE Trans. Image Processing, 8(9), pp. 1161-1174. 1999.
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Published
2003-04-01
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[1]
“Application of symmetric orthogonal multiwavelets and prefilter technique for image compression”, JCS&T, vol. 3, no. 01, pp. p. 47–53, Apr. 2003, Accessed: Mar. 08, 2026. [Online]. Available: https://journal.info.unlp.edu.ar/JCST/article/view/951
