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SPECTRAL RADIUS OF BIORTHOGONAL WAVELETS WITH ITS APPLICATION

Qingyun Zou|Guoqiu Wang|Mengyun Yang
대한수학회 (The Korean Mathematical Society)|2014.09|대한수학회지 (Journal of the KMS)|제51권 제5호|pp. 941-953

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참고문헌

키워드

2-circular matrixbiorthogonalityvanishing momentsfilters of even lengthsimage compression.
주제분류수학

초록

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and ob- tain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

Abstract

In this paper, a 2-circular matrix theory is developed, and a concept of spectral radius for biorthogonal wavelet is introduced. We propose a novel design method by minimizing the spectral radius and ob- tain a wavelet which has better performance than the famous 9-7 wavelet in terms of image compression coding.

참고문헌 (12)

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  2. I. Daubechies, "Orthonormal bases of compactly supported wavelets", Comm. Pure Appl. Math, 41(7), pp.909~996 (1988)
  3. I. Daubechies, "Ten Lectures on Wavelets" (1992), SIAM Pub
  4. H. O. Kim, "Quasi-interpolatory refinable functions and construction of biorthogonal wavelet systems", Adv. Comput. Math, 33(3), pp.255~283 (2010)
  5. T. L. Li, "Characters of circular matrix", Science Bulletin in Chinese, 2, pp.30~33 (1982)
  6. T. Q. Nguyen, "Two-channel perfect reconstruction FIR QMF structures which yield linear-phase analysis and synthesis filters", IEEE Trans. Acoustics Speech Signal Process, 37, pp.676~690 (1989)
  7. A. Said, "A new, fast and efficient image codec based on set partitioning in hierarchical trees", IEEE Trans. Circuits System Video Tech, 6, pp.243~250 (1996)
  8. W. Sweldens, "The lifting scheme: a constructing of second generation wavelet", SIAM. Math. Anal, 29(2), pp.511~546 (1998)
  9. M. Vetterli, "Perfect reconstruction FIR filter banks, some properties and factorizations", IEEE Trans. Acoust. Speech, Signal Process, 37(7), pp.1057~1071 (1989)
  10. G. Q. Wang, "Matrix methods of constructing wavelet filters and discrete hyper-wavelet transforms", Opt. Eng, 39(4), pp.1080~1087 (2000)
  11. G. Q. Wang, "Generic 9-7 tap wavelets filters and their performance studies on image compression", Acta. Electron. Sin, 29, pp.130~132 (2001)
  12. G. Q. Wang, "Optimal model for biorthogonal wavelet filters", Opt. Eng, 42(2), pp.350~356 (2003)

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